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Simplifying radicals numbers
Definitions
Perfect Squares
Multiplying radicals
Rationalize the Denominator
100
Simplify √45
3√5
100

Define Radical

An expression that uses the a root, such as square root or cube root

100

Simplify √9

3

100
Simplify √(6 ) * √(6 )
6
100
1/√5
√5/5
200
Simplify √75
5√3
200

Define Radicand

The number you are finding the root of

200

Simplify √36

6

200

Simplify -4 √15 * - √3

12√5

200
√3/√12
1/2
300

Simplify - √175

-5√7

300

A number that can be made by dividing two integers (an integer is a number with no fractional part). The word comes from "ratio."

Rational

300

Simplify √121

11

300

3√2 x 5√6

30√3

300

√20 / 2√3

√15 / 3

400
Simplify √384
8√6
400

A number made by squaring a whole number

Perfect Square

400

Simplify -√100

-10

400
3√18 (2√8)
72
400

Simplify 3√3 / 4√6 

3√2 / 8

500

Simplify √48x3

4x√3x

500

Define Irrational

A real number that can NOT be made by dividing two integers (an integer has no fractional part). Its decimal also goes on forever without repeating.

500

Simplify -√196

-14
500

3√2 (3 √5)

9√10

500
√16/√25
4/5