MathTV Topic - Roots and Radicals

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Get Ready for College Algebra: Corequisites
Roots and Radicals

Problem 1

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

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Mr. McKeague

Stefanie

Spencer

Julieta

Problem 2

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

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Betsy

Aaron

Edwin

Problem 3

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

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Stefanie

Logan

Cynthia

Problem 4

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

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Nathan

Betsy

Aaron

Edwin

Problem 5

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

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Stefanie

Cynthia

Problem 6

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

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Betsy

Aaron

Edwin

Problem 7

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

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Stefanie

Cynthia

Problem 8

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

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Betsy

Aaron

Edwin

Problem 9

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

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Stefanie

Cynthia

Problem 10

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

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Betsy

Aaron

Edwin

Problem 11

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

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Stefanie

Cynthia

Problem 12

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

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Betsy

Aaron

Edwin

Problem 13

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

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Stefanie

Cynthia

Problem 14

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

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Betsy

Aaron

Edwin

Problem 15

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

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Stefanie

Cynthia

Problem 16

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

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Betsy

Anthony

Problem 17

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

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Stefanie

Cynthia

Problem 18

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

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Stefanie

Cynthia

Problem 19

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

Choose instructor to watch:

Betsy

Anthony

Problem 20

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

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Stefanie

Cynthia

Problem 21

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

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Betsy

Anthony

Problem 22

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

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Stefanie

Cynthia

Problem 23

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

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Stefanie

Aaron

Gordon

Problem 24

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Mr. McKeague

Betsy

Stefanie

Gordon

Problem 25

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

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Betsy

Edwin

Problem 26

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

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Stefanie

Aaron

Gordon

Problem 27

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

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Stefanie

Aaron

Gordon

Problem 28

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

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Betsy

Edwin

Problem 29

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

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Stefanie

Aaron

Julieta

Problem 30

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

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Mr. McKeague

Julieta

Problem 31

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

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Mr. Hampton

Betsy

Stephanie

Edwin

Problem 32

Choose instructor to watch:

Betsy

Cynthia

Problem 33

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

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Betsy

Edwin

Problem 34

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

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Stefanie

Aaron

Gordon

Problem 35

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

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Betsy

Edwin

Problem 36

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

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Julieta

Aaron

Gordon

Problem 37

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

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Betsy

Cynthia

Problem 38

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

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Stefanie

Aaron

Edwin

Problem 39

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

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Stephanie

Sirena

Cynthia

Problem 40

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

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Stefanie

Aaron

Edwin

Problem 41

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

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Stephanie

Sirena

Cynthia

Problem 42

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

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Stefanie

Aaron

Edwin

Problem 43

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

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Sirena

Stephanie

Cynthia

Problem 44

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

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Julieta

Stefanie

Edwin

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