8th Squares, Cubes, Roots, Equations, and Ordering Irrational Numbers

Square and Cube Roots

100

Find the √25.

5

200

What is the 3√216?

6

300

What is the -√144?

-12

400

What is 3√-729?

-9

500

What is the √ 1/64  and the 3√ -1/64  ?

1/8 and - 1/4

Ordering Irrational Numbers

100

List the following in order of least to greatest:  pi , √9, and √4.

√4, √9, and  pi 

200

List the following in order of least to greatest: 3√27, √81, and √1.

√1, 3√27, and √81

300

List the following in order of least to greatest: 3√1,728   2pi  ,√289, and √25.

√25,  2pi , 3√1,728, and √289

400

List the following in order of least to greatest: 0.7², √ 1/4 , 3√ 125/343 and √5.

0.7^2, √ 1/4 , 3√ 125/343 and √5.

500

Place the following in order from least to great2 xx 2/(3*x^2)piest:

 pi ^3, -3√625,  √100, 3√64,000, and -√361

-3√625, -√361, √100,  pi ³, and 3√64,000

Solving Square Root Equations

100

x² = 121

x = 11, -11

200

p² = 196

p = 14, -14

300

g² =  1/9 

g =  1/3 ,  -1/3 

400

n² = 729

n = 27, -27

500

q² =  256/324 

q = 8/9

Solving Cube Root Equations

100

x³ = 64

x = 4

200

m³ = -512

m = -8

300

f³ = 4,913

f = 17

400

b³ =  -1/1000 

b =  -1/10 

500

g³ =  -2744/6859 

 -14/19 = g

Between Which Two...?

100

√14 is between which two numbers?

3 and 4

200

3√63 is between which two numbers?

3 and 4

300

√586 is between which two numbers? Which is it closer to?

24 and 25; closer to 24.

400

The 3√2,710 is between which two numbers? Which one is it closer to?

13 and 14; closer to 14.

500

x² = 784. What are its possible solutions?

x = 28, -28