Operations on Radicals

Simplifying Radicals

100

√32

What is 4√2?

200

sqrt(27)

What is 

3sqrt3

300

sqrt(5^2*11^5)

What is 

605sqrt11

400

sqrt(50)

What is

5sqrt(2x)

500

sqrt(120)

What is 

2sqrt(30)

Multiplying Radicals

100

sqrt(22)*sqrt(8)

What is 4√11

200

sqrt(15x)*sqrt(6)

What is 3√10x

300

sqrt(15)*sqrt(35)

What is 5√21

400

sqrt(7)*sqrt(9)

What is 3√7

500

sqrt(8)*sqrt(27)

What is 6√6

Dividing Radicals

100

sqrt(17/144)

What is 

sqrt(17)/12

200

sqrt(96)/sqrt(12)

What is 2√2

300

sqrt(12)/sqrt(64)

sqrt(3)/4

400

sqrt(65)/sqrt(13)

What is √5

500

sqrt(30)/sqrt(96)

What is 

sqrt(5)/4

Rationalizing the Denominator

100

2/sqrt(6)

What is 

sqrt(6)/3

200

8/sqrt(7)

What is 

(8sqrt(7))/7

300

5/sqrt(2)

What is 

(5sqrt(2))/(2)

400

3/sqrt(3)

What is 

sqrt(3)

500

sqrt((4)/(9)

What is

2/3

Adding and Subtracting Radicals

100

2sqrt(2)+2sqrt(2)

What is 

4sqrt(2)

200

6sqrt(5)-8sqrt(5)

What is 

-2sqrt(5)

300

2sqrt(3)+sqrt(75)

What is 

7sqrt(3)

400

sqrt(32)-sqrt(8)

2sqrt(2)

500

-sqrt(98)+2sqrt(50)

3sqrt(2)