Square/Cube Roots and The Real Number System

Perfect Squares and Cubes

100

Evaluate. 8²

64

200

Evaluate. 10²

100

300

Evaluate. 7³

343

400

Evaluate. 13²

169

500

Evaluate. 9³

729

The Real Number System

100

also known as counting numbers

natural numbers

200

natural numbers plus zero

whole numbers

300

positive and negative whole numbers

integers

400

a number that CAN be written in the form of a/b

rational number

500

a number that CAN'T be written in the form of a/b

irrational 

Roots and Equations

100

Solve. √36

6

200

Solve the equation. x² = 9/49

3/7

300

Solve.  root(3)(-512)  

-8

400

Solve the equation. p³ + 400= 1400

p = 10

500

How are squaring a number and taking its square root related? 

They are inverses (opposites). 

Estimating/Non-Perfect

100

The sqrt(18) is between these two consecutive integers.

4 and 5

200

The sqrt(74) is between these two consecutive integers.

8 and 9

300

The  root(3)(10) is between these two consecutive integers.

2 and 3

400

Which is the larger number? Why?

The sqrt(25) or the root(3)(27)?

sqrt(25) 

sqrt(25) = 5 and root(3)(27) = 3

500

Is √90 a perfect square? Explain.

No, there is no number multiplied by itself that equals 90. 

Rational and Irrational

100

Is π (pi) a rational or irrational number?

irrational

200

Is 3.5 rational or irrational?

rational

300

Is 2/3 rational or irrational?

rational

400

Is √81 rational or irrational? Explain. 

rational, √81 = 9

500

Is √50 rational or irrational? Explain. 

irrational, 50 is not a perfect square