Radicals and Rationalize Denominator
Variable radicals
Area Volume (easy) *don't forget label
Quadratic equations
Triangles
100

12/√7        

12√(7)/ 7

100

√x10

x5

100

A sign is 8 units long and 4 units wide. What is the area of the sign?

32 units 2  

100

24 + x- 10x = 0

x = 6, x = 4

100

A right triangle has a hypotenuse of 6 and legs of 3, 3√3. What are the measures of its angles?

30,60,90

200

√169 + √225

 28

200

√(x12/x4)

x4

200

A pizza has a diameter of 10. What is the area in terms of π?

25 π units2

200

8 + x+ 6x = 0    

x = -4, x = -2

200

A 30, 60, 90 triangle has a hypotenuse of 8. What are the measures of the legs?

 4, 4√3

300

√289- √256

1

300

9x+√x9

9x+x4√x

300

A box has a length of 5 inches, a width of 4 inches, and a height of 2 inches. What is the volume of the box?

40 units 3

300

x2+ 26x + 169 = 0

x = -13

300

A 45,45, 90 triangle has a leg of 8. What are the measures of the other sides?

 8√2, 8

400

7√86-√56    

7√(86) - 2√14

400

2x√(x+ x4)

2x5

400

A circle has a radius of 16. What is the area of the circle in terms of π?

256π units2

400

3x+ 3x - 90 = 0

x = -6, x = 5

400

A triangle has one angle that measures 90 degrees, and one angle that measures 30 degrees. The hypotenuse of the triangle is 16. What is the measure of the third angle and the measure of the legs?

60 degrees, 8, 8√3

500

7√(199-87)√(98/5

Bonus 250 pts: Multiply your answer by 1/70

-762/5

-762/350


500

(√(64x8y12z11))/(20x-6y4z3)

Bonus 250 pts: Multiply your answer by 1/5

(2x10y2z2√z)/5

2x10y2z2√z)/25


500

A cylinder has a radius of 10 and a height of 5. What is the volume of the cylinder in terms of π?

Bonus 250 pts: Whats is the surface area 


500π units 3

300π units 2

500

16x+ 8x - 35    

Bonus 250 pts: Multiply answer by 5

 (4x+7)(4x-5)

80x2+40x-175


500

A right triangle has one angle that measures 60 degrees and a hypotenuse of 18. Find the measures of all the angles and legs of the triangle.

Bonus 250 pts: What is the cosine of the 60-degree angle?

30, 60, 90 degrees, 9, 9√3

1/2

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