Question 1

Simplify $$\sqrt{27} to $$its simplest radical form.

Accepted Answer

$$3\sqrt{3}$$

Question 2

Which of the following is the simplest radical form of $$\sqrt{45}$$?

Accepted Answer

$$3\sqrt{5}$$

Question 3

Simplify $$3\sqrt{8} to $$its simplest radical form.

Accepted Answer

$$6\sqrt{2}$$

Question 4

A chemist needs to simplify $$2\sqrt{27} to $$measure a compound. What is the simplest radical form?

Accepted Answer

$$6\sqrt{3}$$

Question 5

Simplify $$\sqrt{108} to $$its simplest radical form.

Accepted Answer

$$6\sqrt{3}$$

Question 6

A construction worker needs to cut a piece of wood with a length of $$\sqrt{245} cm. $$What is the simplest radical form of this length?

Accepted Answer

$$7\sqrt{5}$$

Question 7

Simplify $$9\sqrt{180} to $$its simplest radical form.

Accepted Answer

$$54\sqrt{5}$$

Question 8

A pharmacist needs to mix $$4\sqrt{125} mg of a $$drug. What is the simplest radical form?

Accepted Answer

$$20\sqrt{5}$$

Question 9

Which of the following expressions is equivalent to $$\sqrt{75}$$? Select all that apply.

Accepted Answer

$$5\sqrt{3}$$

Question 10

Which of the following expressions is equivalent to $$\sqrt{75}$$? Select all that apply.

Accepted Answer

$$\sqrt{25} \cdot \sqrt{3}$$

Question 11

A square garden has an area of $$108$$ square meters. What is the length of one side in simplest radical form?

Accepted Answer

$$6\sqrt{3}$$

Question 12

Simplify $$\sqrt{180} to $$its simplest radical form.

Accepted Answer

$$6\sqrt{5}$$

Question 13

A biologist measures a sample and records $$\sqrt{245}$$ grams. What is the simplest radical form?

Accepted Answer

$$7\sqrt{5}$$

Question 14

Which of the following is the correct simplification of $$\sqrt{125}$$?

Accepted Answer

$$5\sqrt{5}$$

Question 15

If $$x = 3\sqrt{5}$$ and $$y = \sqrt{45}$$, which of the following is true?

Accepted Answer

$$x = y$$

Question 16

A square tile has an area of $$180 cm$^2. $$What is the length of one side in simplest radical form?

Accepted Answer

$$6\sqrt{5}$$

Question 17

Simplify $$2\sqrt{75} to $$its simplest radical form.

Accepted Answer

$$10\sqrt{3}$$

Question 18

Which of the following is equivalent to $$\sqrt{9} \cdot \sqrt{5}$$?

Accepted Answer

$$3\sqrt{5}$$

Question 19

A square plot of land has an area of $$245 m$^2. $$What is the length of one side in simplest radical form?

Accepted Answer

$$7\sqrt{5}$$

Question 20

Simplify $$\sqrt{25} \cdot \sqrt{3} to $$its simplest radical form.

Accepted Answer

$$5\sqrt{3}$$

Step-by-Step Guidance: Simplifying Square Root Expressions

Study Guide - Practice Questions