Radicals Review

Perfect Squares

100

√1

1

200

√9

3

300

√25

5

400

√144

12

500

√169

13

Simplify Radicals

100

√12

√(3*4)
2√3

200

2√27

2√(9*3)

2*3√3

6√3

300

2√125v

2√(25*5)v
2*5√5v
10√5v

400

√80v³

√(16*5)v³

4√5*v*v*v
4v√5v

500

√72

√(9*8)
3√8
3√(4*2)

3*2√2

6√2

Adding Radical Expressions

100

4√6 + 3√6

7√6

200

2√6 - 2√24

2√6 - 2√(6 x 4)

2√6 - 4√6

-2√6

300

-3√17 - 4√17

-7√17

400

-9√3 - 6√3 + 8√3

-7√3

500

-3√12 + 3√20 - 3√8

- 3√(4 x 3) + 3√(4 x 5) - 3√(4 x 2)

-3*2√3 + 3*2√5 - 3*2√2

-6√3 + 6√5 - 6√2

Multiplying Radical Expressions

100

2 * √5

2√5

200

√2 * √8

4

300

√5 * -4√20

-4√100
-4 * 10
-40

400

√20y² * √20y

√400y^{3
*take the square root of 400 out front
*take the square root of 2 of the y's and bring 1 y out front}
20y√y

500

√15n^{2 *} √10n³

√150n⁵
√25 * 6 * n * n * n * n * n
*take perfect square of 25 (5) out front
^* take the perfect square of n⁴ (n²) out front
* you are left with 6 and one n under the radical
5n² √6n

Miscellaneous

100

√x¹⁶

x⁴

200

6√15 - 3√15

3√15

300

4√2 + 2√8 - 3√2

4√2 + 2√(4*2) - 3√2
4√2 + 2√(4*2) -3√2

√2 + 2*2√2
√2 + 4√2
5√2 

400

√13 * √13

√169

13

500

10x√4x * 3x²√8

10x*3x²√(4x*8)
30x³√32x
30x³√(16*2*x)

30x³*4√2x
120x³√2x