Radicals

Simplify radical expressions

100

sqrt(45)

3sqrt5

200

4sqrt(200)

40sqrt(2)

300

sqrt(24x^5y^8)

2x^2y^4sqrt(6x)

400

(54x^10)^(1/3)

3x^3sqrt(2x

500

sqrt(.64)

.8

Operations with radical expressions

100

sqrt(12)+sqrt(27)

5sqrt(3)

200

sqrt(45)-sqrt(20)

sqrt5

300

sqrt(54)+sqrt(108)

3sqrt(6)+6sqrt(3)

400

(sqrt(5)-sqrt(x))(sqrt(5)+sqrt(x))

5-x

500

sqrt(3x)(sqrt(3)+sqrt(3x)+sqrt(x))

3sqrt(x)+3x +xsqrt(3)

Multiple and divide radical expressions

100

sqrt(32)*sqrt(2)

8

200

2sqrt(5)*3sqrt(20)

60

300

(sqrt(x)-sqrt(3))^2

x-2sqrt(3x)+3

400

sqrt(98)/sqrt(2)

7

500

Rationalize the following: 

4/(sqrt(5)-sqrt(4))

4sqrt(5)+8

Solve radical equations

100

sqrt(x+3) = 5

x= 22

200

4sqrt(x)- 7 = 5

x = 9

300

sqrt(4x-3)=sqrt(x+3)

x = 2

400

x = sqrt(4x-7) +1

x = 4,2

500

sqrt(x)-4 = sqrt(x-16)

x = 16

Radical word problems

100

Find the missing side of a right triangle with leg lengths of 10 and 24. 

26

200

Find the missing side of a triangle with one leg length of 5 and a hypotenuse of 9.

2sqrt(14)

300

A flagpole height is 20 feet. If a boy is standing 5 feet from the base of the flagpole, how far is he from the top of the pole?

5sqrt(17)

400

Find the distance between (2,3) and (9,7)

sqrt(65)

500

t = sqrt(d)/4 is the formula for the distance an object falls in t seconds. How long does it take an object to fall from the top of the Sears Tower (1450 feet). Round your answer to the nearest hundredth.

9.52 seconds