Simplifying Radicals

​Simplifying Radicals

Review​

Before we start simplifying radicals, let's review perfect squares.

Multiple Choice

Which of the following is a perfect square?

• 12
• 90
• 40
• 64

Multiple Choice

Which of the following in NOT a perfect square?

• 49

• 81

• 111

• 144

Multiple Choice

144

• is a perfect square.

• is not a perfect square.

Multiple Choice

65

• Is a perfect square.
• Is not a perfect square.

​Review:

To Simplify a Square Root is the process of evaluating the perfect squares that are factors.

Examples

Multiple Choice

$$\sqrt{15}=\sqrt{5}\cdot\sqrt{3}$$  True or False?

• True

• False

How to simplify a radical

Multiple Choice

What is the largest perfect square that you use to simplify

$$\sqrt{24}$$  

• 1

• 4

• 9

• 16

Multiple Choice

Simplify

$$\sqrt{24}$$  

• $$4\sqrt{6}$$  

• $$2\sqrt{6}$$  

• $$6\sqrt{2}$$  

• $$6\sqrt{4}$$  

Multiple Choice

Simplify:

$$\sqrt{98}$$  

• $$7\sqrt{2}$$  

• $$2\sqrt{7}$$  

• $$49\sqrt{2}$$  

• $$2\sqrt{49}$$  

Multiple Choice

$$\sqrt{50}=25\sqrt{2}$$  True or False?

• True

• False

Multiple Choice

$$Simplify:\ \ \sqrt{20}$$  

• $$2\sqrt{10}$$  

• $$4\sqrt{5}$$  

• $$10\sqrt{2}$$  

• $$2\sqrt{5}$$  

What if you have a number on the outside?

Multiple Choice

Simplify:

$$3\sqrt{125}$$  

• $$75\sqrt{3}$$  

• $$8\sqrt{5}$$  

• $$15\sqrt{5}$$  

• $$15\sqrt{25}$$  

What if you have variables?

1. Make sure the variable is an even power
2. If it's not even, subtract one from the exponent and rewrite as a product
3. Take the variable with the even power and divide by 2 - put that on the outside of the radical

​Simplifying Radicals with Variables Raised to a Power

​Even Exponents

​*Divide the exponent by 2

Multiple Choice

How do you simplify a radical with an even exponent?

• Subtract 1 from the exponent

• Divide the exponent by 2

• Leave 1

• Add 1 to the exponent

Multiple Choice

Simplify: $$\sqrt[]{c^6}$$  

• $$c^2$$  

• $$c^3$$  

• $$c^4$$  

Multiple Choice

Simplify: $$\sqrt[]{z^4}$$  

• $$z^2$$  

• $$z^4$$  

• $$z^3$$  

​What do you do if the exponent is odd?​

​Odd Exponent

​Rules:

1. Draw 2 Radicals

2. Subtract 1 - Put in left radical

3. Leave 1 - Put in right radical

4. Divide by 2 - Put in front of radical​

​Rules:

1. Draw 2 Radicals

2. Subtract 1 - Put in left radical

3. Leave 1 - Put in right radical

4. Divide by 2 - Put in front of radical​

Multiple Choice

Simplify:

$$\sqrt{x^{15}}$$  

• $$x^{7.5}$$  

• $$x^{14}\sqrt{x}$$  

• $$x^7\sqrt{x}$$  

Multiple Choice

Simplify: $$\sqrt[]{e^9}$$  

• $$e^5\sqrt[]{e^4}$$  

• $$e^8\sqrt[]{e}$$  

• $$e^4\sqrt[]{e}$$  

​Let's Mix it Up!!!!!

​ Simplify:

​Simplify:

Seperate, Operate, Combine..........SOC THE RADICAL!!!!!

​Combine:

Multiple Choice

Simplify:

$$\sqrt{x^2y^7}$$  

• $$xy^3$$  

• $$xy^3\sqrt{y}$$  

• $$xy^3\sqrt{xy}$$  

Multiple Choice

Simplify:

$$\sqrt{80x^2y^4}$$  

• $$2xy^2\sqrt{20}$$  

• $$4xy^2\sqrt{5}$$  

Multiple Choice

Simplify: $$\sqrt[]{125c^9}$$  

• $$5c^4\ \sqrt[]{5c^5}$$  

• $$5c^4\ \sqrt[]{5c}$$  

• $$25c^4\ \sqrt[]{5c}$$  

Multiple Choice

Simplify: $$\sqrt[]{54c^6d^5}$$  

• $$3c^3d^2\ \sqrt[]{6d}$$  

• $$9c^3d^2\ \sqrt[]{6d}$$  

• $$6c^3d^2\ \sqrt[]{3d}$$  

Draw

Draw how you feel about Simplifying Radicals :)