Simplifying Radicals

Vocab

100

What is a radical?

The symbol that signals to take the square root

200

What is a factor?

The numbers multiplied to get a product

300

What is a square root?

The opposite of squaring 

The factors that, when multiplied by themselves, equal the original number

400

What is the first step to simplifying radicals?

Check if the number is a perfect square

500

What is the second step to simplifying radicals when the number is NOT a perfect square?

Divide by perfect squares 

Simplifyingwithout Variables

100

Simplify √12

2√3

200

Simplify √54

6√6

300

Simplify -3√28

-6√7

400

Simplify 3√125

15√5

500

Simplify: 4√200

40√2

Simplifying Variables

100

Simplify √x⁴

x²

200

Simplify √x⁹

x⁴√x

300

Simplify √y¹⁵

y⁷√y

400

Simplify x√x¹⁰

x⁶

500

Simplify y²√y⁷

y⁵√y

Mixed Problems

100

Simplify √4x²y²

2xy

200

Simplify √9x⁴y⁵ 

3x²y²√y

300

Simplify 2x√10x³y¹⁰

2x³y⁵√10x

400

Simplify √24x⁶y⁴

2x³y²√6

500

Simplify 4y√40x⁵y⁵

 8x²y³√10xy

Adding/Subtracting

100

In order to add radicals, what needs to be the same?

the number under the radical

200

Add the following radicals:

 4√3 + 2√3 + 7√3.

13√3

300

Subtract the following radicals: 

6√10 - √10 

5√10

400

Add the following radicals: 

√40 + √90.

6√10

500

Add the following radicals:

-8√90 + 7√10

-17√10