Q: Which of the following is the correct prime factorization of $$36$$?

$$2 \times 2 \times 3 \times 3$$

Q: Which of the following is the correct process to find $$\sqrt{36}$$ using prime factorization?

Break $$36$$ into $$2 \times 2 \times 3 \times 3$$, pair the factors, and take one from each pair: $$2 \times 3 = 6.$$

Q: Which of the following is a common misconception when finding $$\sqrt{36}$$?

Assuming $$\sqrt{36} = 12$$ because $$6 \times 2 = 12.$$

Q: Which of the following best explains how prime factorization helps in finding the square root of a non-perfect square like $$50$$?

It shows that $$50 = 2 \times 5 \times 5$$, so $$\sqrt{50} = 5\sqrt{2}.$$

Question 1

Which of the following best defines a perfect square?

Accepted Answer

A number that is the square of an integer.

Question 2

What is the principal square root of $$49$$?

Accepted Answer

$$7$$

Question 3

A square-shaped park has an area of $$81$$ square meters. What is the length of one side of the park?

Accepted Answer

$$9$$ meters

Question 4

Which of the following numbers is NOT a perfect square?

Accepted Answer

$$50$$

Question 5

Using prime factorization, what is the simplified form of $$\sqrt{72}$$?

Accepted Answer

$$6\sqrt{2}$$

Question 6

Which statement about the principal square root is correct?

Accepted Answer

It is the non-negative square root of a number.

Question 7

A square tile has an area of $$50 cm$^2. $$Using prime factorization, which of the following is the simplest radical form for the length of one side?

Accepted Answer

$$\sqrt{50} = 5\sqrt{2} cm$$

Question 8

Which of the following is the correct prime factorization of $$36$$?

Accepted Answer

$$2 	imes 2 	imes 3 	imes 3$$

Question 9

If $$x^2 = 64$, what is the principal square root of x^2$?

Accepted Answer

$$8$$

Question 10

Which of the following real-world scenarios requires finding a square root?

Accepted Answer

Calculating the side length of a square field given its area.

Question 11

What is the value of $$\sqrt{16} + \sqrt[3]{27}$$?

Accepted Answer

$$7$$

Question 12

Which of the following is the correct process to find $$\sqrt{36}$$ using prime factorization?

Accepted Answer

Break $$36$$ into $$2 	imes 2 	imes 3 	imes 3$$, pair the factors, and take one from each pair: $$2 	imes 3 = 6.$$

Question 13

Which of the following is the cube root of $$8$$?

Accepted Answer

$$2$$

Question 14

A square painting has an area of $$60$$ square inches. Which of the following is the simplest radical form for the length of one side?

Accepted Answer

$$2\sqrt{15}$$ inches

Question 15

Which of the following statements is TRUE?

Accepted Answer

The square root of $$0 is$$ $$0.$$

Question 16

If $$\sqrt{x} = 5$$, what is the value of $$x$$?

Accepted Answer

$$25$$

Question 17

Which of the following is the correct way to express $$\sqrt{18} in $$simplest radical form?

Accepted Answer

$$3\sqrt{2}$$

Question 18

A square plot of land has an area of $$90 m$^2. $$What is the length of one side in simplest radical form?

Accepted Answer

$$3\sqrt{10} m$$

Question 19

Which of the following is a common misconception when finding $$\sqrt{36}$$?

Accepted Answer

Assuming $$\sqrt{36} = 12$$ because $$6 	imes 2 = 12.$$

Question 20

Which of the following best explains how prime factorization helps in finding the square root of a non-perfect square like $$50$$?

Accepted Answer

It shows that $$50 = 2 	imes 5 	imes 5$$, so $$\sqrt{50} = 5\sqrt{2}.$$

Square Roots and Prime Factorization: Study Notes for Intermediate Algebra

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