Operations on Radicals

Simplifying Radicals

100

√32

What is 4√2?

200

sqrt(27)

What is 

3sqrt3

300

sqrt(a^2b^5)

What is 

ab^2sqrtb

400

sqrt(50x^3y^2)

What is

5xysqrt(2x)

500

sqrt(120w^8x^4y^7)

What is 

2w^4x^2y^3sqrt(30y)

Multiplying Radicals

100

sqrt(22)*sqrt(8)

What is 4√11

200

sqrt(15x)*sqrt(6)

What is 3√10x

300

sqrt(15y^2)*sqrt(35y)

What is 5y√21y

400

sqrt(7x^3)*sqrt(9x)

What is 3x²√7

500

sqrt(8x^3y^2)*sqrt(27x^3y^3)

What is 6x³y²√6y

Dividing Radicals

100

sqrt(17/144)

What is 

sqrt(17)/12

200

sqrt(96x)/sqrt(12)

What is 2√2x

300

sqrt(12x)/sqrt(64)

sqrt(3x)/4

400

sqrt(65x^2)/sqrt(13)

What is x√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(2x)

What is 

(5sqrt(2x))/(2x)

400

3/sqrt(3y)

What is 

sqrt(3y)/y

500

sqrt((4x^3)/(9x)

What is

2/3x

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)