Square Roots and Cube Roots

Rational vs Irrational

100

14

Rational

200

3.1415926535...

Irrational

300

4.22222222...

Rational

400

1243.5393743973112....

Irrational

500

20/4

Rational

Estimating

100

Square Root of 7

3

200

Square Root of 32

6

300

Square Root of 87

9

400

Square Root of 45

7

500

Square Root of 165

13

Solving Equations

100

x³ = 27

x = 3

200

x² = 49

x = +- 7

300

x² = 45

x = +_ Square Root of 45

400

x³ + 6 = -58

x = -4

500

3x² - 7 = 20

x = +-3

Volume or Area

100

The area of a square is 100 in². What are the side lengths of the square?

10 inches

200

The volume of a cube is 343 cm². What are the side lengths of the cube?

7 cm 

300

Steve's living room is shaped like a cube. The total space the room takes up (as a volume) is 12167 ft³. What are the side lengths of the bedroom?

23 feet

400

Mr. Bentley has a square basketball court in his backyard where he throws down 360-EastBay-Windmill-Upside Down dunks. The area of the court is 225 ft². What is the side length of the court?

15 feet

500

Marcus has a rubix cube that is very large. The volume of the cube is 512 cm². What is the length of the edge of a cube? AND what is the area of one side of a cube?

8 cm ; 64 cm²

Perfect Square or Perfect Cube

100

25 

Perfect Square

200

343

Perfect Cube

300

86

Neither

400

64

Both

500

4096

Both