Question 1

Which of the following statements is TRUE regarding the square roots of a positive real number $$a$$?

Accepted Answer

The square roots of $$a$$ are $$\sqrt{a}$$ and $$-\sqrt{a}.$$

Question 2

If $$x^2 = 16$, which of the following lists all possible real solutions for x$?

Accepted Answer

$$x = 4$$ and $$x = -4$$

Question 3

A biologist is measuring the area of a square petri dish and finds it to be $$49 cm$^2. $$What are the possible values for the length of one side of the dish?

Accepted Answer

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

Question 4

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

Accepted Answer

It is the positive value $$\sqrt{a}.$$

Question 5

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

Accepted Answer

$$x = 0$$

Question 6

A physics student calculates the time it takes for an object to fall a certain distance using the formula $$d = \frac{1}{2}gt^2$. If d = 20$ m and g = 10$ m/s^2$, what are the possible values for t$?

Accepted Answer

$$t = 2 s $$and $$t = -2 s$$

Question 7

Which of the following equations has exactly two real solutions?

Accepted Answer

$$x^2 = 25$

Question 8

A square garden has an area of $$100 m$^2. $$Which of the following represents all possible values for the length of one side?

Accepted Answer

$$10 m $$and $$-10 m$$

Question 9

If $$x^2 = a$ where a$$ \u003e 0$$, which of the following is always true?

Accepted Answer

$$x = \sqrt{a} or$$ $$x = -\sqrt{a}$$

Question 10

A chemist needs to find the length of a side of a square filter with an area of $$36 cm$^2. $$Which of the following is correct?

Accepted Answer

The side length can be $$6 cm or$$ $$-6 cm.$$

Question 11

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

Accepted Answer

A number $$x$$ such that $$x^2 = a$.

Question 12

If $$x^2 = 81$, what are the possible values of x$?

Accepted Answer

$$x = 9$$ and $$x = -9$$

Question 13

A square has an area of $$a$$ square units. Which of the following expressions gives all possible values for the side length?

Accepted Answer

$$\sqrt{a}$$ and $$-\sqrt{a}$$

Question 14

If $$x^2 = 49$, which of the following is NOT a solution for x$?

Accepted Answer

$$x = 0$$

Question 15

A square parking lot has an area of $$225 m$^2. $$What are the possible values for the length of one side?

Accepted Answer

$$15 m $$and $$-15 m$$

Square Roots and Their Properties

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