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Intermediate Algebra
Rational Exponents and Radicals

1
Summary

Problem  1

These next videos go with the Chapter Test.  

Assume all variable bases are positive integers and all variable exponents are positive real numbers throughout this test.

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Videos Coming Soon

Problem  2

Simplify: \(27^{-\frac{2}{3}}\)

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Mr. Neufeld cc
Mr. Neufeld
Kendra cc
Kendra
Gordon cc
Gordon
Problem  3

Simnplify: \(\left(\dfrac{25}{49}\right)^{-\frac{1}{2}}\)

Choose instructor to watch:
Mr. Neufeld cc
Mr. Neufeld
Kendra cc
Kendra
Gordon cc
Gordon
Problem  4

Simplify: \(a^{\frac{3}{4}}\cdot a^{-\frac{1}{3}}\)

Choose instructor to watch:
Mr. Neufeld cc
Mr. Neufeld
Kendra cc
Kendra
Gordon cc
Gordon
Problem  5

Simplify: \[\frac{\left(x^{\frac{2}{3}}y^{-3}\right)^{\frac{1}{2}}}{\left(x^{\frac{3}{4}}y^{\frac{1}{2}}\right)^{-1}}\]

Choose instructor to watch:
Mr. Neufeld cc
Mr. Neufeld
Kendra cc
Kendra
Gordon cc
Gordon
Problem  6

Simplify: \(\sqrt{49x^8y^{10}}\)

Choose instructor to watch:
Kendra cc
Kendra
Gordon cc
Gordon
Problem  7

Simplify: \(\sqrt[5]{32x^{10}y^{20}}\)

Choose instructor to watch:
Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  8

Simplify: \[\frac{\left(36a^8b^4\right)^{\frac{1}{2}}}{\left(27a^9b^6\right)^{\frac{1}{3}}}\]

Choose instructor to watch:
Joshua cc
Joshua
Kendra cc
Kendra
Problem  9

Simplify: \[\frac{\left(x^ny^{\frac{1}{n}}\right)^n}{\left(x^{\frac{1}{n}}y^n\right)^{n^2}}\]

Choose instructor to watch:
Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  10

Multiply: \(\;2a^{\frac{1}{2}}\left(3a^{\frac{3}{2}}-5a^{\frac{1}{2}}\right)\)

Choose instructor to watch:
Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  11

Multiply: \(\left(4a^\frac{3}{2}-5\right)^2\)

Choose instructor to watch:
Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  12

Factor: \(\;3x^\frac{2}{3}+5x^\frac{1}{3}-2\)

Choose instructor to watch:
Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  13

Factor: \(\;9x^\frac{2}{3}-49\)

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Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon
Problem  14

Combine: \(\dfrac{4}{x^\frac{1}{2}}+x^\frac{1}{2}\)

Choose instructor to watch:
Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon
Problem  15

Combine: \[\frac{x^2}{\left(x^2-3\right)^\frac{1}{2}}-\left(x^2-3\right)^\frac{1}{2}\]

Choose instructor to watch:
Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon
Problem  16

Write in simplified form: \(\sqrt{125x^3y^5}\)

Choose instructor to watch:
Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon
Problem  17

Write in simplified form: \(\sqrt[3]{40x^7y^8}\)

Choose instructor to watch:
Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon
Problem  18

Write in simplified form: \(\sqrt{\dfrac{2}{3}}\)

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Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon
Problem  19

Write in simplified form: \(\sqrt{\dfrac{12a^4b^3}{5c}}\)

Choose instructor to watch:
Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  20

Combine: \(\sqrt[3]{24a^3b^3}-5a\sqrt[3]{3b^3}\)

Choose instructor to watch:
Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  21

Combine: \(\sqrt[3]{24a^3b^3}-5a\sqrt[3]{3b^3}\)

Choose instructor to watch:
Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  22

Multiply: \[\left(\sqrt{x}+7\right)\left(\sqrt{x}-4\right)\]

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Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  23

Multiply: \[\left(3\sqrt{2}-\sqrt{3}\right)^2\]

Choose instructor to watch:
Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  24

Rationalize the denominator: \[\frac{5}{\sqrt{3}-1}\]

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Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  25

Rationalize the denominator: \[\frac{\sqrt{x}-\sqrt{2}}{\sqrt{x}+\sqrt{2}}\]

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Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  26

Solve for \(x\): \[\sqrt{3x+1}=x-3\]

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Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  27

Solve for \(x\): \[\sqrt[3]{2x+7}=-1\]

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Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  28

Solve for \(x\): \[\sqrt{x+3}=\sqrt{x+4}-1\]

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Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  29

Graph: \(y=\sqrt{x-2}\)

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Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  30

Graph: \(y=\sqrt[3]{x}+3\)

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Kendra cc
Kendra
Joshua cc
Joshua
Gordon cc
Gordon
Problem  31

Solve for \(x\) and \(y\) so that the following equation is true: \[(2x+5)-4i=6-(y-3)i\]

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Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon
Problem  32

Simplify: \[(3+2i)-\left[(7-i)-(4+3i)\right]\]

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Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon
Problem  33

Simplify: \((2-3i)(4+3i)\)

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Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon
Problem  34

Simplify: \((5-4i)^2\)

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Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon
Problem  35

Simplify: \(\dfrac{2-3i}{2+3i}\)

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Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon
Problem  36

Show that \(i^{38}\) can be written as \(-1\).

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Kendra cc
Kendra
Mr. Neufeld cc
Mr. Neufeld
Gordon cc
Gordon

2
Roots and Radical Functions

Problem  1
practice icon

What are the two square roots of \(64\)?

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Mr. McKeague cc
Mr. McKeague
Stefanie cc
Stefanie
Spencer cc
Spencer
Julieta cc espanol spanish
Julieta
Problem  2

Use Property 1 in the book to simplify the expression \(\left(\sqrt{3}\right)^2\)

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Breylor cc
Breylor
Nathan cc
Nathan
Stephanie cc
Stephanie
Problem  3

Use Property 1 in the book to simplify the expression.
\(\left(\sqrt[3]{-11}\right)^3\)

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Breylor cc
Breylor
Nathan cc
Nathan
Stephanie cc
Stephanie
Problem  4

Use Property 1 in the book to simplify the expression.
\(\left(\sqrt[5]{2y}\right)^5\)

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Breylor cc
Breylor
Nathan cc
Nathan
Stephanie cc
Stephanie
Problem  5
practice icon

Simplify if possible: \(\sqrt[3]{-8}\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  6
practice icon

Simplify if possible: \(\sqrt{-4}\)

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Stefanie cc
Stefanie
Logan cc
Logan
Cynthia espanol spanish
Cynthia
Problem  7
practice icon

Simplify if possible: \(\sqrt[5]{-32}\)

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  8
practice icon

Simplify if possible: \(\sqrt[4]{-81}\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  9
practice icon

Simplify if possible: \(-\sqrt{25}\)

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Nathan cc
Nathan
Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  10
practice icon

Simplify the expression, if possible.
\(-\sqrt[3]{-64}\)

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Breylor cc
Breylor
Nathan cc
Nathan
Stephanie cc
Stephanie
Problem  11
practice icon

Simplify as much as possible: \(\sqrt{25a^4b^6}\)

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  12
practice icon

Simplify as much as possible: \(\sqrt[3]{x^6y^{12}}\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  13
practice icon

Simplify as much as possible: \(\sqrt[4]{81r^8s^{20}}\)

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  14
practice icon

Graph \(y=\sqrt{x}\) and \(y=\sqrt[3]{x}\)

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Katherine cc
Katherine
Betsy cc
Betsy
CJ cc
CJ
Julieta cc espanol spanish
Julieta
Problem  15

What is the domain of \(f(x)=\sqrt{x}\)?

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Stephanie cc
Stephanie
Breylor cc
Breylor
Nathan cc
Nathan
Julieta cc espanol spanish
Julieta
Problem  16

What is the domain of \(f(x)=\sqrt[3]{x}+3\)?

Choose instructor to watch:
Stephanie cc
Stephanie
Breylor cc
Breylor
Nathan cc
Nathan
Julieta cc espanol spanish
Julieta
Problem  17

What is the domain of \(f(x)=\sqrt{x+2}\)?

Choose instructor to watch:
Stephanie cc
Stephanie
Breylor cc
Breylor
Nathan cc
Nathan
Julieta cc espanol spanish
Julieta

3
Rational Exponents

Problem  1
practice icon

What are the two square roots of \(64\)?

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Stefanie cc
Stefanie
Spencer cc
Spencer
Julieta cc espanol spanish
Julieta
Problem  2
practice icon

Simplify if possible: \(\sqrt[3]{-8}\)

Choose instructor to watch:
Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  3
practice icon

Simplify if possible: \(\sqrt{-4}\)

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Stefanie cc
Stefanie
Logan cc
Logan
Cynthia espanol spanish
Cynthia
Problem  4
practice icon

Simplify if possible: \(-\sqrt{25}\)

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Nathan cc
Nathan
Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  5
practice icon

Simplify if possible: \(\sqrt[5]{-32}\)

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  6
practice icon

Simplify if possible: \(\sqrt[4]{-81}\)

Choose instructor to watch:
Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  7
practice icon

Simplify as much as possible: \(\sqrt{25a^4b^6}\)

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  8
practice icon

Simplify as much as possible: \(\sqrt[3]{x^6y^{12}}\)

Choose instructor to watch:
Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  9
practice icon

Simplify as much as possible: \(\sqrt[4]{81r^8s^{20}}\)

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  10
practice icon

Write as a root, then simplify: \(8^{\frac{1}{3}}\)

Choose instructor to watch:
Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  11
practice icon

Write as root, then simplify: \(36^{\frac{1}{2}}\)

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  12
practice icon

Write as a root, then simplify: \(-25^{\frac{1}{2}}\)

Choose instructor to watch:
Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  13
practice icon

Write as a root, then simplify: \((-25)^{\frac{1}{2}}\)

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  14
practice icon

Write as a root, then simplify: \(\left(\dfrac{4}{9}\right)^{\frac{1}{2}}\)

Choose instructor to watch:
Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  15
practice icon

Write as a rational exponent and simplify: \(\sqrt[3]{x^6y^{12}}\)

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  16
practice icon

Write as a rational exponent and simplify: \(\sqrt[4]{81r^8s^{20}}\)

Choose instructor to watch:
Betsy cc
Betsy
CJ cc
CJ
Anthony espanol spanish
Anthony
Problem  17
practice icon

Simplify as much as possible: \(8^{\frac{2}{3}}\)

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  18
practice icon

Simplify as much as possible: \(25^{\frac{3}{2}}\)

Choose instructor to watch:
Betsy cc
Betsy
Anthony cc
Anthony
Anthony espanol spanish
Anthony
Problem  19
practice icon

Simplify as much as possible: \(9^{-\frac{3}{2}}\)

Choose instructor to watch:
Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  20
practice icon

Simplify as much as possible: \(\left(\dfrac{27}{8}\right)^{-\frac{4}{3}}\)

Choose instructor to watch:
Betsy cc
Betsy
Anthony cc
Anthony
Anthony espanol spanish
Anthony
Problem  21
practice icon

Simplify as much as possible: \(x^{\frac{1}{3}}\cdot x^{\frac{5}{6}}\)

Choose instructor to watch:
CJ cc
CJ
Stefanie cc
Stefanie
Cynthia espanol spanish
Cynthia
Problem  22
practice icon

Simplify as much as possible: \(\left(y^{\frac{2}{3}}\right)^{\frac{3}{4}}\)

Choose instructor to watch:
Betsy cc
Betsy
Anthony cc
Anthony
Anthony espanol spanish
Anthony
Problem  23
practice icon

Simplify as much as possible: \(\dfrac{z^{\frac{1}{3}}}{z^{\frac{1}{4}}}\)

Choose instructor to watch:
CJ cc
CJ
Stefanie cc
Stefanie
Cynthia espanol spanish
Cynthia
Problem  24
practice icon

Simplify as much as possible: \[\left(\frac{a^{-\frac{1}{3}}}{b^{\frac{1}{2}}}\right)^6\]

Choose instructor to watch:
Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia
Problem  25
practice icon

Simplify as much as possible: \(\dfrac{\left(x^{-3}y^{\frac{1}{2}}\right)^4}{x^{10}y^{\frac{3}{2}}}\)

Choose instructor to watch:
Betsy cc
Betsy
Anthony cc
Anthony
Anthony espanol spanish
Anthony
Mini Lecture

Mini Lecture
Simplify each expression:

  1. \(\sqrt[3]{27a^{12}}\)

  2. \(\sqrt[4]{16a^{12}b^{20}}\)

  3. \((-8)^{\frac{1}{3}}\)

  4. \(25^{\frac{3}{2}}\)

  5. \(81^{-\frac{3}{4}}\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague

4
Simplifying Radicals

Problem  1
practice icon

Write \(\sqrt{50}\) in simplified form.

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Gordon espanol spanish
Gordon
Problem  2
practice icon

Write in simplified form: \(\sqrt{48x^4y^3}\), where \(x\), \(y\geq0\).

Choose instructor to watch:
Betsy cc
Betsy
CJ cc
CJ
Mr. Martinez espanol spanish
Mr. Martinez
Problem  3
practice icon

Write \(\sqrt[3]{40a^5b^4}\) in simplified form.

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Gordon espanol spanish
Gordon
Problem  4
practice icon

Write \(\sqrt{12x^7y^6}\) in simplified form.

Choose instructor to watch:
Betsy cc
Betsy
CJ
CJ
Julieta cc espanol spanish
Julieta
Problem  5
practice icon

Write \(\sqrt[3]{54a^6b^2c^4}\) in simplified form.

Choose instructor to watch:
Stefanie
Stefanie
Aaron cc
Aaron
Gordon espanol spanish
Gordon
Problem  6
practice icon

Simplify \(\sqrt{\displaystyle\frac{3}{4}}\)

Choose instructor to watch:
Betsy cc
Betsy
CJ cc
CJ
Mr. Martinez espanol spanish
Mr. Martinez
Problem  7
practice icon

Simplify \(\sqrt{\displaystyle\frac{5}{6}}\)

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Gordon espanol spanish
Gordon
Problem  8
practice icon

Rationalize the denominator in \(\displaystyle\frac{4}{\sqrt{3}}\)

Choose instructor to watch:
Betsy cc
Betsy
CJ cc
CJ
Mr. Martinez espanol spanish
Mr. Martinez
Problem  9

Rationalize the denominator in \(\displaystyle\frac{2\sqrt{3x}}{\sqrt{5y}}\)

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Julieta cc espanol spanish
Julieta
Problem  10
practice icon

Rationalize the denominator in \(\displaystyle\frac{7}{\sqrt[3]{4}}\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Julieta
Julieta
CJ cc
CJ
Julieta cc espanol spanish
Julieta
Problem  11
practice icon

Simplify \(\sqrt{\displaystyle\frac{12x^5y^3}{5z}}\)

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Gordon espanol spanish
Gordon
Problem  12
practice icon

Simplify, but do not assume the variable represents a positive number. \[\sqrt{9x^2}\]

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Betsy cc
Betsy
Stephanie cc
Stephanie
Mr. Martinez espanol spanish
Mr. Martinez
Problem  13
practice icon

Simplify, but do not assume the variable represents a positive number. \[\sqrt{x^3}\]

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Gordon espanol spanish
Gordon
Problem  14
practice icon

Simplify, but do not assume the variable represents a positive number. \[\sqrt{x^2-6x+9}\]

Choose instructor to watch:
Betsy cc
Betsy
CJ cc
CJ
Mr. Martinez espanol spanish
Mr. Martinez
Problem  15
practice icon

Simplify, but do not assume the variable represents a positive number. \[\sqrt{x^3-5x^2}\]

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Gordon espanol spanish
Gordon
Problem  16

Simplify: \(\sqrt[3]{(-2)^3}\)

Choose instructor to watch:
Betsy cc
Betsy
CJ cc
CJ
Mr. Martinez espanol spanish
Mr. Martinez
Problem  17

Simplify: \(\sqrt[3]{\left(-5\right)^3}\)

Choose instructor to watch:
Julieta cc
Julieta
Aaron cc
Aaron
Gordon espanol spanish
Gordon

5
Addition and Subtraction of Radical Expressions

Problem  1
practice icon

Combine \(5\sqrt{3}-4\sqrt{3}+6\sqrt{3}\)

Choose instructor to watch:
Betsy cc
Betsy
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  2
practice icon

Combine \(3\sqrt{8}+5\sqrt{18}\)

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  3
practice icon

Combine \(7\sqrt{75xy^3}-4y\sqrt{12xy}\), where \(x\), \(y\geq 0\).

Choose instructor to watch:
Betsy cc
Betsy
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  4
practice icon

Combine \(10\sqrt[3]{8a^4b^2}+11a\sqrt[3]{27ab^2}\)

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  5
practice icon

Combine \(\dfrac{\sqrt{3}}{2}+\dfrac{1}{\sqrt{3}}\)

Choose instructor to watch:
Betsy cc
Betsy
CJ
CJ
Mr. Martinez espanol spanish
Mr. Martinez
Problem  6

Construct a golden rectangle from a square of side length \(4\). Then show that the ratio of the length to the width is the golden ratio \(\displaystyle\frac{1+\sqrt{5}}{2}\).

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez

6
Multiplication and Division of Radical Expressions

Problem  1
practice icon

Multiply \(\left(3\sqrt{5}\right)\left(2\sqrt{7}\right)\)

Choose instructor to watch:
Stephanie cc
Stephanie
Sirena cc
Sirena
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  2
practice icon

Multiply \(\sqrt{3}\left(2\sqrt{6}-5\sqrt{12}\right)\)

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  3
practice icon

Multiply \(\left(\sqrt{3}+\sqrt{5}\right)\left(4\sqrt{3}-\sqrt{5}\right)\)

Choose instructor to watch:
Stephanie cc
Stephanie
Sirena cc
Sirena
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  4
practice icon

Expand and simplify: \(\left(\sqrt{x}+3\right)^2\)

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  5
practice icon

Expand: \(\left(3\sqrt{x}-2\sqrt{y}\right)^2\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Mrs. Diaz cc
Mrs. Diaz
CJ cc
CJ
Julieta cc espanol spanish
Julieta
Problem  6
practice icon

Expand and simplify: \(\left(\sqrt{x+2}-1\right)^2\)

Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  7
practice icon

Multiply \(\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)\)

Choose instructor to watch:
Sirena cc
Sirena
Stephanie cc
Stephanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  8
practice icon

Divide \(\displaystyle\frac{6}{\sqrt{5}-\sqrt{3}}\) (Rationalize the denominator)

Choose instructor to watch:
Julieta cc
Julieta
Stefanie cc
Stefanie
Mr. Martinez espanol spanish
Mr. Martinez
Problem  9
practice icon

Rationalize the denominator \(\displaystyle\frac{\sqrt{5}-2}{\sqrt{5}+2}\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Mrs. Diaz cc
Mrs. Diaz
CJ cc
CJ
Julieta cc espanol spanish
Julieta
Take 5

Roots and Radicals 6: More Golden Rectangles within Our Orginal

How many Golden Rectangles are contained in any Golden Rectangel?  An infinite number.

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Mr. McKeague cc
Mr. McKeague
Stefanie cc
Stefanie
Julieta espanol spanish
Julieta
Mr. Martinez espanol spanish
Mr. Martinez

7
Radical Equations and Functions

Problem  1
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Solve for \(x\): \(\sqrt{3x+4}=5\)

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Molly S. cc
Molly S.
Betsy cc
Betsy
CJ cc
CJ
Octabio espanol spanish
Octabio
Problem  2
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Solve: \(\sqrt{4x-7}=-3\)

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Stefanie cc
Stefanie
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  3
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Solve \(\sqrt{5x-1}+3=7\)

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Molly S. cc
Molly S.
Betsy cc
Betsy
CJ cc
CJ
Octabio espanol spanish
Octabio
Problem  4
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Solve: \(t+5=\sqrt{t+7}\)

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Molly S. cc
Molly S.
Stefanie cc
Stefanie
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  5
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Solve: \(\sqrt{x-3}=\sqrt{x}-3\)

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Octabio cc
Octabio
Molly S. cc
Molly S.
Cynthia espanol spanish
Cynthia
Octabio espanol spanish
Octabio
Problem  6
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Solve: \(\sqrt{x+1}=1-\sqrt{2x}\)

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Stefanie cc
Stefanie
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  7
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Solve: \(\sqrt{x+1}=\sqrt{x+2}-1\)

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Betsy cc
Betsy
CJ cc
CJ
Julieta cc espanol spanish
Julieta
Problem  8
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Solve \(\sqrt{2x-10}=\sqrt{x-4}+\sqrt{x-12}\)

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Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia
Problem  9
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Solve: \(\sqrt[3]{4x+5}=3\)

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Stefanie cc
Stefanie
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  10
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Graph \(y=\sqrt{x}\) and \(y=\sqrt[3]{x}\)

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Katherine cc
Katherine
Betsy cc
Betsy
CJ cc
CJ
Julieta cc espanol spanish
Julieta

8
Complex Numbers

Problem  1
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Write in terms of \(i\): \(\sqrt{-25}\)

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Stefanie cc
Stefanie
Betsy cc
Betsy
Julieta cc espanol spanish
Julieta
Problem  2
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Write in terms of \(i\): \(\sqrt{-49}\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  3
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Write in terms of \(i\): \(\sqrt{-12}\)

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Betsy cc
Betsy
Stefanie cc
Stefanie
CJ cc
CJ
Julieta cc espanol spanish
Julieta
Problem  4
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Write in terms of \(i\): \(\sqrt{-17}\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  5
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Simplify as much as possible: \(i^{30}\)

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Stefanie cc
Stefanie
CJ cc
CJ
Julieta cc espanol spanish
Julieta
Problem  6
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Simplify as much as possible: \(i^{11}\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  7
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Simplify as much as possible: \(i^{40}\)

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  8
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Find \(x\) and \(y\) if \(3x+4i=12-8yi\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  9
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Find \(x\) and \(y\) if \((4x-3)+7i=5+(2y-1)i\)

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Jesse cc
Jesse
Stefanie cc
Stefanie
CJ cc
CJ
Julieta cc espanol spanish
Julieta
Problem  10
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Simplify: \((3+4i)+(7-6i)\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  11
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Simplify: \((7+3i)-(5+6i)\)

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  12
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Simplify \((5-2i)-(9-4i)\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  13
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Multiply: \((3-4i)(2+5i)\)

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  14
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Multiply: \(2i(4-6i)\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  15
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Expand: \((3+5i)^2\)

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  16
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Multiply: \((2-3i)(2+3i)\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez
Problem  17
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Divide: \(\dfrac{2+i}{3-2i}\)

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Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  18
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Divide: \(\dfrac{7-4i}{i}\)

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Betsy cc
Betsy
Aaron cc
Aaron
Mr. Martinez espanol spanish
Mr. Martinez