Free Printable MC 8.2 - Simplifying nth Roots

1.

Simplify the radical...

√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

2.

Simplify

√45n³

a)

3n√5n

b)

4n√8

c)

4n√-8

d)

10√n

3.

a)

y²z¹⁰√xy

b)

20yz√xy

c)

xy²z¹⁰√y

d)

yz⁶√xy²z²

4.

Simplify

a)

A

b)

B

c)

C

d)

D

5.

√45x⁴y⁷

a)

3x²y³√5

b)

9x²y³√5y

c)

3x²y³√5y

d)

3x⁴y⁷

6.

a)

x³√x

b)

7x√x²

c)

x⁶√x

d)

√x

7.

a)

x⁴y⁴√y

b)

72xy

c)

xy√y

d)

x²y³√x²

8.

a)

xy√y

b)

x²y²√y

c)

xy√xy

d)

2x2y√y

9.

a)

2x³y¹⁰√y

b)

2x³y⁷

c)

x³y¹⁰√2y

d)

2x⁵y¹⁰√xy

10.

a)

2x¹²y¹⁸√6

b)

12x¹²y¹⁸

c)

2x¹²y⁶√6

d)

12x¹²y6

11.

a)

9x⁴√x

b)

9x³

c)

3x⁴√2x

d)

3x³√2

12.

a)

x⁵y¹⁰√xy

b)

x³√y¹⁰

c)

x⁶y²⁰

d)

x³y¹⁰

13.

Simplify the following:

a)

A

b)

B

c)

C

d)

D

14.

Simplify the following:

a)

A

b)

B

c)

C

d)

D

15.

Simplify the following:

a)

A

b)

B

c)

C

d)

D

16.

Simplify the following:

a)

A

b)

B

c)

C

d)

D

17.

a)

A

b)

B

c)

C

d)

D

18.

a)

A

b)

B

c)

C

d)

D

19.

Simplify $\sqrt[\ ]{16x^{12}y^{16}}$

a)

$8x^6y^4$

b)

$4x^{10}y^{14}$

c)

$4x^6y^4$

20.

Simplify $\sqrt[3]{27x^9y^{12}}$

a)

$3x^3y^4$

b)

$9x^3y^4$

c)

$3x^6y^9$

21.

Simplify $\sqrt[4]{81x^4y^{12}}$

a)

$9x^2y^3$

b)

$3y^8$

c)

$3xy^3$

22.

$2\sqrt{27}+8\sqrt{3}+5\sqrt{8}$

a)

$24\sqrt{3}$

b)

$24\sqrt{3}+5\sqrt{8}$

c)

$14\sqrt{3}+10\sqrt{2}$

d)

$14\ \sqrt[]{3}+3\ \sqrt[]{8}$

23.

$\sqrt[3]{16}-\sqrt[3]{250}$

a)

$3\ \sqrt[]{-234}$

b)

$-3\sqrt[3]{2}$

c)

$7\sqrt[3]{2}$

d)

$3\sqrt[3]{2}$

24.

$5\sqrt{200}-5\sqrt{8}$

a)

$60\sqrt{2}$

b)

$\sqrt{8}$

c)

$40\sqrt{2}$

d)

$2\ \sqrt[]{2}$

25.

Find the area of the rectangle

a)

11

b)

$22\ +3\sqrt{6}$

c)

$22+\sqrt{42}-2\sqrt{6}$

d)

$34+11\sqrt{6}$

26.

$3\sqrt[4]{96}-\sqrt[4]{486}-\sqrt[]{2}$

a)

$3\ \sqrt[4]{6}-2\ \sqrt[]{2}$

b)

$9\sqrt[4]{6}-3\ \sqrt[]{2}$

c)

$3\sqrt[4]{6}-3\ \sqrt[]{2}$

d)

$3\sqrt[4]{6}-\sqrt[]{2}$

27.

$\sqrt[]{15x}\left(5\ \sqrt[]{6}-5\ \sqrt[]{5x}\right)$

a)

$-15x\ \sqrt[]{5x}+5$

b)

$15\ \sqrt[]{10x}-25x\ \sqrt[]{3}$

c)

$-8\ \sqrt[]{2x}+8x\ \sqrt[]{x}$

d)

$10x\ \sqrt[]{3}-12x\ \sqrt[]{5x}$

28.

$3\sqrt[3]{40}+3\sqrt[3]{40}$

a)

$24\sqrt[3]{5}$

b)

$12\sqrt[3]{5}$

c)

$18\sqrt[3]{5}$

d)

$6\sqrt[3]{5}$

29.

$2\ \sqrt[]{27}+2\ \sqrt[]{3}$

a)

$0$

b)

$-2\ \sqrt[]{3}$

c)

$2\ \sqrt[]{3}$

d)

$8\ \sqrt[]{3}$

30.

Which number is the index?

a)

3

b)

4

c)

5

31.

We get NO SOLUTIONS when we have a negative number under radical and ______

a)

the index is ODD

b)

the index is EVEN

MC 8.2 - Simplifying nth Roots

Total questions: 31

Worksheet time: 48mins

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