Question 1

Which of the following best describes the radicand in the radical expression $$5 \sqrt[3]{7}$$?

Accepted Answer

The number 7

Question 2

Simplify $$\sqrt{108x$$^{16}$$}.$$

Accepted Answer

$$6x^8$$\sqrt{3}$$

Question 3

Which of the following is a true statement about the square root of a negative number?

Accepted Answer

It is not a real number.

Question 4

Simplify $$\sqrt{16x^4$y^{11}$$}$.

Accepted Answer

$$4x^2y^5$\sqrt{y}$

Question 5

Which of the following is the correct simplification of $$\sqrt{50}$$?

Accepted Answer

$$5\sqrt{2}$$

Question 6

What is the result of $$\sqrt{2x^2$} \cdot \sqrt{8x}$$?

Accepted Answer

$$4x\sqrt{2x}$$

Question 7

Which property allows you to combine $$x^m \cdot x^n$$ into a single term?

Accepted Answer

Product Rule for Exponents: $$x^m \cdot x^n = x$$^{m+n}$$

Question 8

Simplify $$\sqrt{75} + \sqrt{12} - 3\sqrt{3}.$$

Accepted Answer

$$2\sqrt{3}$$

Question 9

Which of the following is the correct simplification of $$\sqrt[3]{64x^6$}$$?

Accepted Answer

$$4x^2$$

Question 10

A chemist needs to dilute a solution and ends up with a concentration of $$\sqrt{18}$$ grams per liter. What is the simplified form of this concentration?

Accepted Answer

$$3\sqrt{2}$$ grams per liter

Question 11

Which of the following is the correct way to rationalize the denominator of $$\frac{1}{\sqrt{3}}$$?

Accepted Answer

$$\frac{\sqrt{3}}{3}$$

Question 12

Simplify $$\sqrt{245y^5$z^{16}$$}$.

Accepted Answer

$$7y^2z^8$\sqrt{5y}$

Question 13

Which of the following is the correct simplification of $$\sqrt[4]{625b$$^{28}$$k^{23}$$}$?

Accepted Answer

$$5|b^7$k^5$$|\sqrt[4]{$$k^3$$}$

Question 14

Which of the following is a true statement about cube roots?

Accepted Answer

Cube roots can be taken of negative numbers and the result is negative.

Question 15

Simplify $$\frac{\sqrt{50x^6$}}{\sqrt{4x^4$}}.$$

Accepted Answer

$$\frac{5x}{2}$$

Question 16

A medical researcher is analyzing a sample and finds the value $$\sqrt[3]{-27}. $$What is the simplified value?

Accepted Answer

$$-3$$

Question 17

Which of the following is the correct simplification of $$\sqrt{98k}$$?

Accepted Answer

$$7\sqrt{2k}$$

Question 18

Which of the following is the correct way to express $$\sqrt[3]{x^6$}$$?

Accepted Answer

$$x^2$$

Question 19

Which of the following is the correct simplification of $$\sqrt{128n^8$}$$?

Accepted Answer

$$8n^4$$\sqrt{2}$$

Question 20

Which of the following is the correct simplification of $$\sqrt{16y^2$}$$?

Accepted Answer

$$4|y|$$

Radicals and Roots: Structure, Simplification, and Operations

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