Dividing Radicals and Rationalizing Denominators

Unit 4: Continue Radicals Rationalize the Denominator

By Stephanie Balbaneda

Write down the following practice problems down!

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Have your notebook out and ready

​Lets review some problems from last class!

Some text here about the topic of discussion

Multiple Choice

What do you call this mathematical expression?

• fraction

• radical

• exponent

• binomial

Multiple Select

Which of the following is an example of radical expression?

• $$x^2$$

• $$3x=y$$

• $$b^{\frac{1}{2}}$$

• $$\sqrt{y}$$

Multiple Choice

√48

• 4√2
• 6√3
• 4√3
• 4√2

Multiple Choice

Simplify the following radical: 2√24

• 4√6
• 2√6
• 24√2
• 4√4

Multiple Choice

• 7√3
• Can't Simplify
• 6√15
• 6√3

Multiple Choice

Simplify:
√6 ⋅√6

• √36
• 2√3
• 12
• 6

Multiple Choice

 Simplify:   2√40 - 3√10 

• 5√10
• √10
• -√30

Multiple Choice

$$4\sqrt{6}\cdot\sqrt{3}$$  

• $$4\sqrt{9}$$  

• $$\sqrt{72}$$  

• $$4\sqrt{18}$$  

• $$12\sqrt{3}$$  

Multiple Choice

$$\sqrt{6}\left(2\sqrt{6}\right)$$  

• 12

• $$12\sqrt{6}$$  

• $$2\sqrt{36}$$  

• $$\sqrt{72}$$  

Rationalizing the Denominator

The objective is to have no square roots in the denominator. To do that we perform multiplication to the ratio that will remove the square root (cancel it) from the denominator.

Subject | Subject

Rationalize the Denominator

Multiple Choice

Simplify: $$\frac{2}{\sqrt[]{2}}$$  

• $$\sqrt[]{2}$$  

• $$\frac{15}{5}$$  

• $$\frac{2\sqrt[]{5}}{3}$$  

• $$\frac{\sqrt[]{2}}{2}$$  

Multiple Choice

Simplify: $$\frac{\sqrt[]{2}}{4\sqrt[]{3}}$$  

• $$\frac{\sqrt[]{15}}{9}$$  

• $$\frac{2\sqrt[]{3}}{3}$$  

• $$\frac{\sqrt[]{6}}{12}$$  

• $$2\sqrt[]{6}$$  

Multiple Choice

Rationalize the denominator. $$\frac{\sqrt{3}}{\sqrt{15}}$$  

• $$\frac{\sqrt{5}}{5}$$  

• $$\frac{\sqrt{3}}{12}$$  

• $$\frac{5\sqrt{2}}{2}$$  

• $$\frac{\sqrt{3}}{3}$$  

Multiple Choice

Rationalize the denominator. $$\frac{\sqrt{4}}{\sqrt{5}}$$  

• $$\frac{\sqrt{10}}{5}$$  

• $$\frac{2\sqrt{5}}{5}$$  

• $$\frac{\sqrt{5}}{2}$$  

• $$\frac{\sqrt{15}}{3}$$  

Multiple Choice

Rationalize the denominator. $$\frac{4}{\sqrt{5}}$$  

• $$\frac{4\sqrt{5}}{5}$$  

• $$\frac{\sqrt{5}}{4}$$  

• $$\frac{\sqrt{6}}{3}$$  

• $$\frac{5\sqrt{2}}{2}$$