Question 1

Which of the following statements about the square roots of positive real numbers is correct?

Accepted Answer

Every positive real number has two square roots, one positive and one negative.

Question 2

What is the principal square root of $$16$$?

Accepted Answer

$$4$$

Question 3

If $$x is a $$positive real number, which equation correctly represents its two square roots?

Accepted Answer

$$\sqrt{x}$$ and $$-\sqrt{x}$$

Question 4

Which of the following best describes the solution set to $$x^2 = 25$?

Accepted Answer

$$x = 5$$ and $$x = -5$$

Question 5

A chemical reaction requires a temperature that is the square root of $$81$$ degrees Celsius. What are the possible temperatures?

Accepted Answer

$$9$$ and $$-9$$

Question 6

If $$x^2 = 9$, which of the following is NOT a solution?

Accepted Answer

$$x = 0$$

Question 7

In a physics experiment, the displacement is given by $$d^2 = 36$. What are the possible values for d$?

Accepted Answer

$$d = 6$$ and $$d = -6$$

Question 8

Which of the following is the correct definition of a square root?

Accepted Answer

A number that, when squared, equals the original number.

Question 9

If $$x is a $$positive real number, which statement is true about $$x$$ and its square roots?

Accepted Answer

$$x$$ has two square roots: one positive and one negative.

Question 10

A historical event occurred in the year $$y$$ such that $$y^2 = 196$. What are the possible values for y$?

Accepted Answer

$$y = 14$$ and $$y = -14$$

Question 11

Which of the following is the principal square root of $$100$$?

Accepted Answer

$$10$$

Question 12

If $$x^2 = 64$, what are the two possible values for x$?

Accepted Answer

$$x = 8$$ and $$x = -8$$

Question 13

Which equation correctly shows the relationship between a number and its square roots?

Accepted Answer

$$x^2 = n$ \Rightarrow x = \sqrt{n} or$$ $$x = -\sqrt{n}$

Question 14

If $$x^2 = 1$, what are the possible values for x$?

Accepted Answer

$$x = 1$$ and $$x = -1$$

Question 15

A student is asked to find all square roots of $$4. $$Which answer is correct?

Accepted Answer

$$2$$ and $$-2$$

Question 16

Which of the following is NOT a square root of $$9$$?

Accepted Answer

$$0$$

Question 17

If $$x is a $$positive real number, which of the following statements is FALSE?

Accepted Answer

$$x$$ has only one square root.

Question 18

A real-life scenario involves finding the square roots of $$25$$ for a financial calculation. What are the possible values?

Accepted Answer

$$5$$ and $$-5$$

Square Roots and Their Properties

Study Guide - Practice Questions