The Number System

Rational/Irrational

100

A rational number can be written as a __________________, and either _______________ OR _________________________.

fraction, repeats or terminates

200

An _________________number can NOT be written as a fraction. It never repeats OR terminates.

Irrational

300

Any number that is NOT a perfect square is ____________________________

irrational

400

Which numbers are RATIONAL?

7²       5.645...       7.223       34/789      Pi

7², 7.223, 34/789

Solving Equations

100

When solving equations, I need to __________________ the variable.

isolate (get it by itself)

200

To isolate the variable, I use ____________ ________________________.

opposite operations

300

x³ = 512 SHOW YOUR WORK.

x = 8

400

Square root of x = 11. SHOW YOUR WORK.

121

Estimating

100

True or False: I need to estimate all perfect cubes.

FALSE

200

The first step in estimating a non-perfect square is to find _____________________

which two perfect squares the number falls between

300

Estimate the square root of 220. SHOW ALL WORK.

14.7, 14.8, 14.9

400

Estimate the cube root of 835. SHOW ALL WORK.

9.4, 9.3, 9.2

Ordering and Comparing

100

Turn all numbers into ______________________ in order to order them.

decimals

200

Compare. Fill in the correct symbol: <, >, =

SHOW YOUR WORK!

12/7          1.823

<

300

Order these from greatest to least. SHOW YOUR WORK!

3.92         2²            78/21

2², 3.92, 78/21

400

Order these from least to greatest. SHOW YOUR WORK!

6.8     square root 55       cube root 90       84/14

Cube root 90, 84/14, 6.8, square root 55

Word Problems

100

Matthew is building a square fire pit. His fire pit has an area of 81ft². How many feet of bricks will he need for ONE side of his fire pit? SHOW YOUR WORK.

9 feet of bricks

200

Hunter's game cube has a volume of 729in³. Will his game cube fit on his square table that has a side length of 13 inches? EXPLAIN. SHOW YOUR WORK!

Yes - Hunter's game cube only takes up 9 inches!

300

Cadence has a square sticker with side lengths of 7 inches. Will her sticker fit on her paper that has an AREA of 26 inches? SHOW YOUR WORK. EXPLAIN.

No - the paper has side lengths of approx. 5.09 inches. 7 inches is larger than 5.09 inches

400

Layla has 2 cubes that she is stacking for her lizard. One cube has a volume of 64in³ and the other one has a volume of 27in³. What is the TOTAL HEIGHT of the stacked cubes? SHOW YOUR WORK! 

7 inches