Unit 1 Review

Real Numbers

100

Is √36 rational or irrational?

Rational, because √36 = 6. 

200

Classify -8 using all real-number sets that apply.

Integer, rational, real.

300

Is 0.454545.... rational or irrational? Explain.

Rational because it is a repeating decimal.

400

Order from least to greatest:

√10, π, 3.2 

*Use inequality signs for extra 100 points*

π < √10 < 3.2

500

Which number does not belong with the others? Explain.

√49, −8/4 , 0.125, √11 

√11, because it is irrational. The others are rational.

Square Roots

100

Simplify √64

8

200

Simplify √20

2√5

300

Simplify √72

6√2

400

Simplify √180

6√5

500

Simplify  3√48 - 2√27

3*4√3 −2*3√3 = 12√3 −6√3 = 6√3

GCF & LCM

100

Find the GCF:

18,24 

6

200

Find the LCM:

8,12 

24

300

Find the GCF:

18x⁴y²,30x³y⁵

6x³y²

400

Find the LCM:

6a²b³,15a⁴b 

30a⁴b³

500

Find both the GCF and LCM:

24x³y² , 36x²y⁵

GCF: 12x²y²
LCM: 72x³y⁵

Exponent Rules

100

Simplify:

x⁴ ⋅ x³ 

x⁷

200

a⁹/a⁴

a⁵

300

Simplify:

(3x⁴)(5x⁷) 

15x¹¹

400

 Simplify:

24x⁹y⁶ / 6x³y²

4x⁶y⁴

500

Simplify 

(18a⁸b⁵/3a²b³) ⋅ 2a³b

12a⁹b³

Power Up

100

 Simplify:

(x³)⁴

x¹²

200

Rewrite using positive exponents:

x⁻⁵ 

1/x⁵

300

 Simplify:

(2x³)⁴ 

16x¹²

400

Simplify using only positive exponents:

x⁻³y⁵ / y²

y³/x³

500

 Simplify completely using positive exponents:

(2x³y⁻²)² / 4x⁻¹y

4x⁶y⁻⁴ / 4x^-1y = x⁶⁻⁽⁻¹⁾y⁻⁴⁻¹ = x⁷y⁻⁵ = x⁷/y⁵