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Simplifying Radicals (square, cube, and fourth roots)

Total questions: 15

Worksheet time: 8mins

Name
Class
Date
1.

Simplify the radical

a)

33

b)

20.2520.25

c)

99

d)

1212

2.

Simplify the radical

a)

1313

b)

9898

c)

1414

d)

1212

3.

Simplify the radical

a)

5 ∛25\ ∛2

b)

2 ∛52\ ∛5

c)

83 ∛383\ ∛3

d)

25 ∛225\ ∛2

4.

Simplify the radical

a)

5 ∜25\ ∜2

b)

2 ∜52\ ∜5

c)

2020

d)

4 54\ \sqrt{5}

5.

Simplify the radical

a)

2302\sqrt{30}

b)

3 203\ \sqrt{20}

c)

3403\sqrt{40}

d)

4 304\ \sqrt{30}

6.

Simplify the radical

a)

1010

b)

10 ∛310\ ∛3

c)

3 ∛103\ ∛10

d)

33 ∛333\ ∛3

7.

Simplify the radical

a)

∣x∣ ∜x2\left|x\right|\ ∜x^2

b)

x2 ∜xx^2\ \ ∜x

c)

x2 ∜x2x^2\ \ ∜x^2

d)

x ∜xx\ \ ∜x

8.

Simplify the radical

a)

y4\sqrt{y^4}

b)

∣y4∣\ \left|y^4\right|

c)

y4 y^4\

d)

y2 y2y^2\ \sqrt{y^2}

9.

Simplify the radical

a)

az2 ∛zaz^2\ ∛z

b)

az ∛z2az\ ∛z^2

c)

z2 ∛azz^2\ ∛az

d)

az2 ∛azaz^2\ ∛az

10.

Simplify the radical

a)

∣g3∣h2 ∜h\left|g^3\right|h^2\ \ ∜h^{ }

b)

∣g3h2∣ ∜h\left|g^3h^2\right|\ ∜h

c)

h ∜g3h2h\ ∜g^3h^2

d)

h2 ∜g3hh^2\ ∜g^3h^{ }

11.

Simplify the radical

a)

j7∣k2∣jj^7\left|k^2\right|\sqrt{j}

b)

j7jk2j^7\sqrt{jk^2}

c)

j2jk7j^2\sqrt{jk^7}

d)

jk2j7jk^2\sqrt{j^7}

12.

Simplify the radical

a)

m3n5 ∛mp2m^3n^5\ ∛mp^2

b)

mp2 ∛m3n5mp^2\ ∛m^3n^5

c)

m ∛m3n5p2m\ ∛m^3n^5p^2

d)

m3n5p ∛mm^3n^5p\ ∛m

13.

Simplify the radical

a)

7f3 ∛f7f^3\ ∛f

b)

7f37f^3

c)

f3 ∛7ff^3\ ∛7f

d)

7f7f

14.

Simplify the radical

a)

2w3x ∜2wx2w^3x\ ∜2wx

b)

2w∣x∣ ∜2w32w\left|x\right|\ ∜2w^3

c)

8wx ∜2w38wx\ ∜2w^3

d)

4wx ∜2w34wx\ ∜2w^3

15.

Simplify the radical

a)

3y2z77y3y^2z^7\sqrt{7y}

b)

3y∣z7∣7y3y\left|z^7\right|\sqrt{7y}

c)

9yz77y9yz^7\sqrt{7y}

d)

3yz73yz3yz^7\sqrt{3yz}