Rules for Square Roots

Square and Cubed Roots Review

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Square roots --- come from the SQUARE shape

Under the square root symbol is the "area" of the square

The square root (answer) is the side length of the square because ____ x______ = the area and since it is a square the number is the same.

The answer could be positive or negative.

Cubed Roots

Come from the shape of a CUBE which has three dimensions so it is ___ x ___ x ___ = volume of a cube

So the answer will always be positive because you cannot multiply 3 negatives and get a positive answer.

Multiple Choice

Which of the following is NOT a perfect square?

• 1

• 4

• 100

• 8

Multiple Choice

√196 = ______

• $$\pm$$  14

• 14²
• 15
• 15²

Multiple Choice

Mr. Jarowski is hanging a square picture frame that has an area of 169 cm². Find the total length of the frame.

• 12 cm

• 52 cm

• 13 cm

• 16 cm

Multiple Choice

The area of the square pool on Mr. Carr's vacation was 256 ft². How long was one side of the pool?

• 17 ft

• 18 ft

• 16 ft

• 15 ft

Multiple Choice

What is the cube root of 125?

• 5
• -5
• 25
• -25

Multiple Choice

∛216

• 6
• 72
• 108
• 4

Multiple Choice

To find the square root of a number, you must divide it by 2.

• True
• False

Multiple Choice

$$\sqrt{16}=?$$  

• 8

• 2

• $$\pm$$  4

• 32

Multiple Choice

$$9^2=18$$  True or false?

• True

• False

Multiple Choice

$$3_{\sqrt{8}}$$    (cube root of 8) 

• 2

• $$\pm2$$  

• -2

• None of the above 

Multiple Choice

√40 is between

• 8 and 9
• 7 and 8
• 5 and 6
• 6 and 7

Multiple Choice

200

• is a perfect square

• is not a perfect square

Multiple Choice

∛125

• 5
• 4
• 6
• 7

Multiple Choice

Solve the following.

x²=25

• x=12.5

• x=50

• x=±5

• x=25

Multiple Choice

Solve the following.

x³=512

• x=8

• x=256

• x=170

• x=1536

Multiple Choice

x²=-64

• x=±8

• x=-8

• x=8

• Cannot be done

Multiple Choice

x³=-27

• x=3

• x=27

• x=-3

• x=54

Multiple Choice

Which number is not a perfect cube?

• 8

• 30

• 125

• 216

Multiple Choice

Leona is so excited. Her grandma is ordering a cubic hot tub that has a volume of 216 ft³. Her grandma needs to know how long each side is to order trim. What is the length of each side?

• 4 feet

• 6 feet

• 8 feet

• 108 feet

Multiple Choice

Valencia, Saralyn, and Emily are solving math problems to win a race. They need to determine the approximate value of  $$\sqrt{47}$$ . Saralyn insists the value is closer to 7, while Emily is sure it is closer to 8. Valencia thinks the value is closer to 6. Who do you agree with?

• Saralyn 

• Emily

• Valencia

Multiple Choice

Evaluate.±

• ±13
• ±14
• 14
• 13

Multiple Choice

Between what two integers would you find the value of √150?

• 12 and 13
• 11 and 12
• 13 and 14
• 15 and 16

Multiple Choice

What are the square roots of 36?

• 6 and -6
• 6
• -6

Multiple Choice

Which of these is both a perfect square and a perfect cube?

• 64

• 125

• 225

• 81

Multiple Choice

Solve for p when p² = 100.

• 1,000
• $$\pm$$  10

• 10

• -0.10

Multiple Choice

Solve for x when x³ = 125

• 5
• 10
• 12
• 15

Multiple Choice

The volume of a cube is 1,000 cm³. What is the length of each side of the cube? 

• 1
• 10
• 100
• 300

Multiple Choice

The √21 is between which two integers?

• 5 and 6

• 20 and 22

• 4 and 5

• 10 and 11