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

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

Accepted Answer

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

Question 3

A medical dosage calculation requires finding the square root of $$49. $$What are the possible values for the dosage?

Accepted Answer

$$7$$ and $$-7$$

Question 4

Which of the following best describes the principal root of a positive real number $$a$$?

Accepted Answer

The positive square root of $$a$$

Question 5

If $$x^2 = 25$, what are the possible values of x$?

Accepted Answer

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

Question 6

A chemical reaction requires a temperature such that $$T^2 = 81$. What are the possible values for T$?

Accepted Answer

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

Question 7

Which of the following is NOT a square root of $$36$$?

Accepted Answer

$$0$$

Question 8

If $$y is a $$positive real number, which of the following statements is true?

Accepted Answer

$$y$$ has two square roots, one positive and one negative.

Question 9

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

Accepted Answer

$$14$$ and $$-14$$

Question 10

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

Accepted Answer

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

Question 11

If $$a is a $$positive real number, which of the following is always true?

Accepted Answer

$$\sqrt{a} \u003e 0$$

Question 12

Which equation correctly shows that both $$3$$ and $$-3$$ are square roots of $$9$$?

Accepted Answer

$$3^2 = 9$ and (-3)^2$ = 9$$

Question 13

If $$x is a $$positive real number, which of the following is NOT a square root of $$x$$?

Accepted Answer

$$x$$

Question 14

A real-life scenario: The area of a square garden is $$64$$ square meters. What are the possible values for the length of one side?

Accepted Answer

$$8$$ meters and $$-8$$ meters

Square Roots and Their Properties in College Algebra

Study Guide - Practice Questions