Rational Numbers and Roots

Rational/Irrational

100

Is a terminating decimal rational or irrational? 

Give an example of a terminating decimal. 

Rational

3.4

200

Give an example of an irrational number. 

0.1254327032945633....

pi

Square root of 2

300

Classify the number -6 as rational, integer, whole number, natural number, or rational. It can be more than one. 

Rational and Integer

400

Explain why the square root of 5 is irrational. 

Because 5 is not a perfect square. Or the square root of 5 is a decimal that does not terminate or does not end.

500

Tell whether each number is rational or irrational. 

5 

-1/2

3.4593829582034...

0.333333...

Rational

Rational

Irrational

Rational 

Vocabulary

100

What is a repeating decimal? 

A decimal that has a number or group of numbers that repeat. 

200

What is a perfect cube? 

Give an example of a perfect cube. 

The result of multiplying a number by itself 3 times. 

Example: 8

300

Define square root. 

The side length of a square. Or the number the you multiply to itself twice to get a perfect square.

400

What is a terminating decimal? 

A decimal in which the numbers after the decimal point ends or terminates. 

500

Define an irrational number.

An irrational number is a number that cannot be written as a fraction. The decimal form does not terminate or repeat. 

Square Roots

100

What is the square root of 121? 

11

200

What is the negative square root of 64

-8

300

What is the square root of 1/25?

1/5

400

If a square has an area of 100, what are the side lengths of the square? 

10

500

Explain why you can not take the square root of a negative number. 

A negative times a negative is positive. 

A positive times a positive is positive. 

Therefore, you can not multiply two numbers together and get a negative perfect square. 

Cube Roots

100

What is the cube root of -512? 

-8

200

Is 342 a perfect cube? 

No

300

What is the cube root of 1/1331? 

1/11

400

What is the next perfect cube after 8? 

27

500

What is the cube root of -1000?

-10

Evaluating Root Expressions/Estimation

100

Estimate the square root of 29 to the nearest tenth. 

No calculator

5.4

200

Solve the expression below. 

2(square root of 25) - 5

5

300

Solve the expression below. 

(square root of 32)² - 11

21

400

Estimate the square root of 125. 

No calculator

11.2

500

2/7 + square root of 1/16

15/28