8.23.1.2-Simplifying Square Roots-Advancing Lesson

Simplifying Square Roots

By Susan Joyce

Method 1

1. Find the largest perfect square that is a factor of the number

2. Write the factor pair under the square root (radical) sign

3. Write as the product of two separate square roots

4. Take the square root of the perfect square. Keep the other number under the radical.​

​

​Simplify Square Roots

Multiple Choice

Simplify $$\sqrt{45}$$  

What is the largest perfect square that is a factor of 45? 9

Write your number as the product of the perfect square and the other number.

$$\sqrt[]{9\times5}$$  

Simplify.

• $$9\sqrt{5}$$  

• $$5\sqrt{9}$$  

• $$3\sqrt{5}$$  

• $$5\sqrt{3}$$  

Multiple Choice

 Simplify $$\sqrt{84}$$  

What is the largest perfect square that is a factor of 84? 4

Write your number as the product of the perfect square and the other number.

$$\sqrt[]{4\ x\ 21}$$  

Simplify.

• $$4\sqrt{21}$$  

• $$2\sqrt{21}$$  

• $$21\sqrt{2}$$  

• $$21\sqrt{4}$$  

Multiple Choice

Simplify $$\sqrt{150}$$  

What is the largest perfect square that is a factor of 150? 25

Write 150 as a product of the perfect square and its other factor.

$$\sqrt[]{25\times6}$$  

Simplify.

• $$5\sqrt{6}$$  

• $$6\sqrt{5}$$  

• $$10\sqrt{15}$$  

• $$3\sqrt{75}$$  

Multiple Select

Select all perfect square factors

• 9

• 3

• 6

• 64

• 25

Multiple Choice

Select all perfect square factors

• 5

• 100

• 144

• 200

• 121

Multiple Choice

Simplify $$\sqrt{242}$$  

What is the largest perfect square that is a factor of 242? 121

Write 242 as factor of the perfect square and the other factor.

$$\sqrt[]{121\times2}$$  

Simplify.

• $$2\sqrt{11}$$  

• $$11\sqrt{2}$$  

• $$4\sqrt{23}$$  

• $$2\sqrt{11}$$  

Multiple Choice

Simplify $$\sqrt{54}$$  

What is the largest perfect square that is a factor of 54? 9

Write 54 as a factor of the perfect square and the other factor.

$$\sqrt[]{9\times6}$$  

Simplify

• $$9\sqrt{6}$$  

• $$6\sqrt{3}$$  

• $$6\sqrt{9}$$  

• $$3\sqrt{6}$$  

Fill in the Blanks

Which are the best factors to use to simplify $\sqrt{200}$  ?

Multiple Choice

Simplify $$\sqrt{500}$$  

Use either method.

• $$4\sqrt{125}$$  

• $$5\sqrt{10}$$  

• $$10\sqrt{5}$$  

• $$10\sqrt{50}$$  

Multiple Choice

Simplify $$\sqrt{108}$$  

Use either method.

• $$3\sqrt{6}$$  

• $$6\sqrt{3}$$  

• $$36\sqrt{3}$$  

• $$3\sqrt{36}$$  

Let's Practice