Cube Roots

Evaluating Square and Cube Roots

Learning Objectives: - To be able to evaluate square roots

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- To be able to evaluate cube roots

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- To be able to evaluate expressions in real world

problems

​Examples:

Multiple Choice

The √ symbol is called the radical.

• True
• False

Multiple Choice

A perfect square is a number whose square root is ___________.

• Even

• irrational

• Rational

• Odd

Multiple Choice

The Principal square root is the _____________.

• Absolute Value
• Positive Square Root
• Negative Square Root
• Opposite Square Root

Multiple Choice

Square roots are the opposite of ____________.

• Cube Roots

• Squaring

• Multiplication

• Absolute Value

Multiple Choice

True or false? 9² is 18

• True
• False

Multiple Choice

Is 225 a perfect square?

• Yes
• No

Multiple Choice

Find the square root.
±√144

• 11, -11
• 16, -16
• 13, -13
• 12, -12

Multiple Choice

(-7)² =

• -14

• 49

• 14

• -49

Multiple Choice

-7² =

• -14

• 49

• $$\frac{25}{13}$$  

• -49

Multiple Choice

The square root of: $$\frac{625}{169}$$  

• $$\frac{25}{16}$$  

• $$\frac{15}{13}$$  

• $$\frac{25}{13}$$  

Multiple Choice

If I know the area of a square, how do I find the side length?

• I square the area.
• I divide the area by 2.
• I take the square root of the area.
• I divide the area by 4.

Multiple Choice

x² = 121
What does x equal?

• 11²
• 11 and -11
• $$\frac{25}{13}$$  

• 12 and 1

Multiple Choice

2² = _____

• 2
• 6
• 4
• 16

Multiple Choice

$$\sqrt[]{-25}$$  

• 5

• -5

• $$\pm5$$  

• No root exists

Multiple Choice

• √81 = 9
• 9 ÷ 9 = 1
• 9 × 2 = 18
• √9 = 3

​Cube Roots and Perfect Cubes

​A perfect cube is an integer that is the cube of an integer; in other words, it is the product of an integer multiplied by itself 3 times.

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​For example: 125 is a perfect cube, since it is an integer, whose cube root 5, is also an integer.

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​5 x 5 x 5 = 125

​Examples:

Multiple Choice

Cube Roots are the opposite of:

• Square Roots

• Cubing

• Squaring

• Multiplying

Multiple Choice

What is 2 cubed?

2³

• 8

• 6

• 4

• 16

Multiple Choice

Which number is both a perfect square and a perfect cube?

• 64

• 27

• 81

• 16

Multiple Choice

Evaluate ∛1

• 1

• 2

• 3

• 4

Multiple Choice

∛125

• 5
• 4
• 6
• 7

Multiple Choice

What is the cube root of 27?

• 9
• 3
• -3
• -9

Multiple Choice

What number, n, cubed is equal to 64?

n³ = 64

• 4

• 2

• 8

• 262,144

Multiple Choice

∛-64

• -4

• 4

• $$\pm4$$  

• -8

Multiple Choice

$$\sqrt[3]{\frac{8}{27}}$$  

• $$\frac{2}{3}$$  

• $$-\frac{2}{3}$$  

• No cube root exists

• $$\frac{2}{27}$$  

Multiple Choice

$$\sqrt[3]{-\frac{8}{125}}$$  

• $$\frac{2}{5}$$  

• $$-\frac{2}{5}$$  

• No root exists

Poll

Rate your understanding of this lesson:

• I feel great about this lesson

• I understand some ideas, but need some practice

• I need a lot more time to review this lesson

​Time to work on ALEF Lessons 17 and 18

• ​​Complete the Check Your Understanding Sections for ALEF Lesson 17

• ​Complete the Exit Ticket for ALEF Lesson 17

• ​​Complete the Check Your Understanding Sections for ALEF Lesson 18

• ​Complete the Exit Ticket for ALEF Lesson 18