Question 1

Which of the following numbers is an irrational number?

Accepted Answer

$$\sqrt{2}$$

Question 2

Which of the following is the correct radical form for $$27^{\frac{2}$${3}}$$?

Accepted Answer

$$\sqrt[3]{27^2$}$$

Question 3

A cube has a volume of $$200 cm$^3. $$What is the edge length of the cube written as a radical in simplest form?

Accepted Answer

$$\sqrt[3]{200}$$

Question 4

Simplify the expression $$\sqrt{80}.$$

Accepted Answer

$$4\sqrt{5}$$

Question 5

Which of the following is equivalent to $$x^{-\frac{3}$${2}}$$?

Accepted Answer

$$\frac{1}{x$$^{\frac{3}$${2}}}$$

Question 6

Which of the following statements is TRUE?

Accepted Answer

All natural numbers are integers.

Question 7

Express $$3\sqrt{5} as an $$entire radical.

Accepted Answer

$$\sqrt{45}$$

Question 8

Which of the following is the correct simplification of $$\sqrt[3]{54}$$?

Accepted Answer

$$3\sqrt[3]{2}$$

Question 9

A biologist uses the formula $$b = 0.01m$$^{\frac{2}$${3}} to $$estimate the brain mass $$b (kg) of a $$mammal with body mass $$m (kg). $$What is the brain mass of a polar bear with $$m = 200 kg$$? (Round to two decimal places)

Accepted Answer

$$0.34 kg$$

Question 10

Which of the following is a rational number?

Accepted Answer

$$\frac{8}{27}$$

Question 11

Simplify the expression $$(x^3y^2$)(x^2y$$^{-4}$$)$.

Accepted Answer

$$x^5y$$^{-2}$

Question 12

Which of the following is the correct radical form for $$a^{\frac{m}$${n}}$$?

Accepted Answer

$$\sqrt[n]{a^m}$$

Question 13

Which of the following is the correct simplification of $$\sqrt{200}$$?

Accepted Answer

$$10\sqrt{2}$$

Question 14

Which of the following is the correct simplification of $$\frac{0.8^2$}{0.8^7$}$$?

Accepted Answer

$$0.8^{-5}$$

Question 15

Which of the following is the correct simplification of $$(a^2b^3$)^4$$?

Accepted Answer

$$a^8b$$^{12}$

Question 16

Which of the following is the correct simplification of $$\sqrt[4]{162}$$?

Accepted Answer

$$3\sqrt[4]{2}$$

Question 17

Which of the following is the correct simplification of $$\sqrt[3]{144}$$?

Accepted Answer

$$2\sqrt[3]{18}$$

Question 18

Which of the following is the correct simplification of $$\sqrt[3]{32}$$?

Accepted Answer

$$2\sqrt[3]{4}$$

Question 19

Which of the following is the correct simplification of $$\sqrt[3]{500}$$?

Accepted Answer

$$5\sqrt[3]{4}$$

Question 20

Which of the following is the correct simplification of $$\sqrt[4]{405}$$?

Accepted Answer

$$3\sqrt[4]{5}$$

Roots and Powers: Rational and Irrational Numbers, Radicals, and Exponent Laws

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