Roots & Irrational Numbers

The Real Numbers

100

Which numbers are irrational?

-5/12,   0.15,   π ,  √5 , √25 

 π ,  √5

200

Give an example of a repeating decimal

0.333...,   1.63333 

300

Rational Numbers are rational because they can be expressed as __________

fractions and decimals 

400

Irrational Numbers are so because they ... 

never end and never repeat 

500

How the terms perfect square and square root related?

 A perfect square is the square of a whole number. The positive square root of a whole number is a whole number. 

Classify Numbers

100

RATIONAL OR IRRATIONAL?  Explain your reasoning.

3.216

RATIONAL because it terminates.

200

What set(s) of numbers does  -sqrt81  fall into?

Natural, whole, integers, rational

RATIONAL, INTEGER

300

pi

IRRATIONAL

400

RATIONAL OR IRRATIONAL?  Explain your reasoning.

6²

Rational because 36 is a whole number 

500

Is sqrt2/2  rational or irrational?

IRRATIONAL

Equations with roots

100

x^2=121

What is 11, -11?

200

(x + 2)^2=16 

2

300

121 is a perfect square 

False

400

 sqrt36  +  2sqrt25

16

500

The cube of 7

343

Roots

100

sqrt36=

6

200

+-sqrt25=

5, -5 or 

+-5

300

root3(-8)=

-2

400

Estimate sqrt12 to the closest integer.

3

500

Round to nearest thousandths 

 sqrt4587

67.727

Estimate Square Roots

100

√53

7

200

√10

3

300

Compare √ 6 and √ 7

>, <, or =?

√6 < √7

400

Which 2 whole numbers is the √ 5 and √ 8?

2 and 3

500

The area of a square is √ 75 square inches.  Estimate the side length to the nearest tenth.  

8.7