Unit 2 Review

Rational vs. Irrational

100

Determine if the following number is rational or irrational: 

The square root of 25

Rational because the square root of 25 is 5. 

200

Determine if the following number is rational or irrational: 

The square root of 11

Irrational because the square root of 11 is a non-terminating decimal.

300

Determine if the following number is rational or irrational: 

8.2121212121

8.21 is a rational number because it is a repeating decimal

400

Define irrational

Irrational numbers are decimals that do not terminate or repeat

Square roots that are not perfect squares are irrational numbers

500

Define Rational

Rational numbers are integers, decimals that terminate or repeat, fractions that convert to repeating or terminating decimals, and perfect square roots 

Estimating Roots

100

Round the the closest tenth

The square root of 24

~ 4.9

200

The square root of 125 is closest to which integer?

11

300

The square root of 38 is between which two integers?

6 and 7

400

Find the square root of 38 and round the nearest tenth

~ 6.2

500

Estimate to the nearest tenth

The square root of 28

~28.09

Solving Equations

100

5x - 10 = 25

x = 7

200

16 = v/3 + 8

v = 24

300

Determine if the equation has one solution, no solution, or infinite solutions:

5 - 8b = -8(b - 1)

5 = 1

No solution

400

2 - 8x = 6x - 4(-1+3x)

x = -12

500

8y + 18 = -2(-4y - 9)

All real numbers 

Scientific Notation

100

Write in standard notation:

7.34 x 10^6

7,340,000

200

Write in scientific notation: 

0.000254

2.54 x 10^-4

300

(3.4 x 10^-6)(2.8 x 10^3)

9.52 x 10^-3

400

(8.6 x 10^7)

___________

(4.3 x 10^9)

2 x 10^-2

500

(8 x 10^2) ^ 3

512 x 10^8 = 

5.12 x 10^10

Exponents

100

Simplify:

3^5 x 3^-5

3^0 = 1

200

2n^2 x 2n^2

4n^4

300

Solve: 

3 ^ -4

1/81

400

Solve:

12 ^-6 x 12^5

12^-1 =1/12^1 = 1/12

500

Solve: 

4^2 x 3^3 x 6^-2

16 x 27 / 36 = 432/36 = 12