Radicals

Conjugates

100

Simplify 

4/(2+sqrt7)

What is 

(-8+4sqrt7)/3

200

Simplify 

6/(3-sqrt2)

What is

(18+6sqrt2)/7

300

Simplify 

5/(2+sqrt7)

What is 

(-10+5sqrt7)/3

400

Simplify 

8/(3+sqrt3)

What is 

4-(4sqrt3)/3

500

What did bob do wrong while simplifying  

4/(3-sqrt2)

 if his final expression was          

(12+4sqrt2)/(9+sqrt2 + sqrt2)

     ?

What is he left the square root expression in the denominator and did not multiply.

Simplifying Radical Expressions

100

Simplify 

sqrt(4x)*sqrt5

What is 

2sqrt(5x)

200

Simplify 

sqrt72

What is 

6sqrt2

300

Simplify 

sqrt44

What is 

2sqrt11

400

Simplify 

sqrt48

What is 

4sqrt3

500

Simplify 

sqrt18 * sqrt4

What is 

6sqrt2

Operations with Radical Expressions

100

Simplify 

sqrt2 * sqrt10

What is 

5sqrt2

200

Simplify 

(3sqrt20)/sqrt4

What is 

3sqrt5

300

Simplify 

2sqrt98+4sqrt32

What is 

30sqrt2

400

Simplify 

sqrt24-sqrt54+9sqrt6

What is 

8sqrt6

500

Simplify

4sqrt5*(2sqrt3 + 7sqrt5)

What is 

8sqrt15 + 140

Application

100

The surface area S of a sphere with a radius r is given by the formula 

S=4pir^2

Solve the formula for r. Then find the radius of a globe with a surface area of 804 square inches.

What is 

r=sqrt(S/(4pi))

; about 8 in

200

A storage container has the shape of a rectangular prism. Its height is 6 feet. Its length is two times its width. The volume is 288 cubic feet. Find the length and width of the container. 

What is 

width: 

sqrt24 approx4.9 ft

length:

2sqrt24 approx9.8 ft

 

300

The surface area S of a cube with side length a is given by the formula 

S=6a^2

Solve the formula for a. Then approximate the side length of a cube with a surface area of 724 square inches. 

What is 

a=sqrt(S/6)

about 11 inches

400

The volume V of a cylinder with radius r and height h is given by the formula 

V=pir^2h

Solve the formula for r. Then find the radius of a cylinder with a height of 15 centimeters and a volume of 750 cubic centimeters.  

What is

r=sqrt(V/(pih)

about 4 centimeters 

500

root(3)9 * root(3)6

3root(3)2 

Simplifying the nth Root

100

Simplify 

6root5(10)*root3(8) * 3root5(5)

What is 

36root5(50)

200

Solve 

sqrt(100)/sqrt(4)

5/2

300

Solve 

sqrt(50x^5)/sqrt(2x)

5x²

400

Simplify 

2sqrt5 + 7sqrt10 - 3sqrt20

What is 

-4sqrt5 + 7sqrt10

500

Solve 

root(3)(54a^3b^5)/root(3)(16a^2b^2)

 

(3broot(3)a)/2