Question 1

Which of the following best describes the radicand in the expression $$\sqrt{25}$$?

Accepted Answer

The number under the radical sign, which is 25

Question 2

What is the principal (positive) square root of $$49$$?

Accepted Answer

$$7$$

Question 3

Evaluate $$\sqrt{-36}.$$

Accepted Answer

Imaginary

Question 4

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

Accepted Answer

It is always an imaginary number.

Question 5

What is the value of $$\sqrt{\frac{1}{4}}$$?

Accepted Answer

$$\frac{1}{2}$$

Question 6

Evaluate $$\sqrt{(-5)^2$}.$$

Accepted Answer

$$5$$

Question 7

Which of the following is the correct definition of the $$nth $$root of a number $$a$$?

Accepted Answer

$$b^n = a$$

Question 8

Evaluate $$\sqrt[3]{-8}.$$

Accepted Answer

$$-2$$

Question 9

Which of the following is true about even-index roots of negative numbers?

Accepted Answer

They are always imaginary numbers.

Question 10

If $$\sqrt[4]{16} is $$evaluated, what is the principal root?

Accepted Answer

$$2$$

Question 11

Which of the following expressions is imaginary?

Accepted Answer

$$\sqrt{-25}$$

Question 12

What is the value of $$\sqrt[3]{125}$$?

Accepted Answer

$$5$$

Question 13

If $$x^n$$ has an exponent equal to the index, what is the result?

Accepted Answer

The exponent and index cancel, leaving just $$x.$$

Question 14

Which of the following is a perfect square?

Accepted Answer

$$36$$

Question 15

Evaluate $$\sqrt[4]{-81}.$$

Accepted Answer

Imaginary

Question 16

Which of the following is the correct way to write the $$nth $$root of $$a$$?

Accepted Answer

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

Question 17

If $$\sqrt[3]{-27} = x$$, what is the value of $$x$$?

Accepted Answer

$$-3$$

Question 18

Which of the following is NOT a perfect cube?

Accepted Answer

$$16$$

Question 19

What is the value of $$\sqrt[5]{-32}$$?

Accepted Answer

$$-2$$

Question 20

A chemist needs to find the cube root of the volume $$V = 1000 cm$^3 to $$determine the side length of a cube-shaped container. What is the side length?

Accepted Answer

$$\sqrt[3]{1000} = 10 cm$$

Roots and Radicals: Square Roots, nth Roots, and Imaginary Numbers

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