Exponents and Roots Review

Exponents

100

Solve: 6²

36

200

Simplify:  17⁴ x 17²²

17²⁶

300

Solve:  3^-4

1/81

400

Simplify: (15⁹ * 15¹¹)⁶

15¹²⁰

500

[(-2)⁵ / (3² - 12⁰)]^-3

- (1/64)

(alternate answers: -1/64; 1/-64)

Scientific Notation

100

What is 8390000000 in scientific notation?

8.39 * 10⁹

200

What is 7.654 * 10^-4 in standard notation?

.0007654

300

(4.2 * 10¹³) * (1.1 * 10⁷)

4.62 * 10²⁰

400

(1.96 * 10⁴) / (7 * 10⁹)

Please state your answer in scientific notation.

2.8 * 10^-6

500

(1.2892 * 10⁹) - (3.369 * 10⁶)

Please state your answer in scientific notation. 

1.285831 * 10⁹

Square Roots

100

What is the square root of 9?

3

200

What two whole numbers will the square root of 7 fall between?

2 and 3

300

The square root of 4/9, times the square root of 81/16

1 1/2 

or 3/2

or 1.5

400

Find the approximate square root of 27 (Answer should be rounded to the nearest hundredth)

5.22 (the twos will keep repeating)

500

Find the approximate square root of 111 (Answer should be rounded to the nearest hundredth)

10.52

Pythagorean Theorem

100

Side A is 3 meters. Side B is 4 meters. What is Side C?

5 meters

200

A triangle has sides with the lengths 7, 9, and 12. Is it a right triangle?

No. 7² + 9² does not equal 12²

300

You have a right triangle with a leg that's 8 feet long and a hypotenuse that's 10 feet long. How long is the other leg?

6 feet long

400

You drive from your house to your friend's house by going 8 miles north and then 15 miles west. How far away is your friend's house along a straight path?

17 miles

500

How far apart are the following points:

(-5, 9) and (18, -3)

(you can state your answer as "the square root of ____")

The square root of 673

(approximately 25.94)

Real, Rational, Irrational

100

What is the difference between a rational number and an irrational number?

Rational numbers can be written as decimals that terminate or repeat. Irrational numbers can only be written as decimals that continue on with no apparent pattern.

200

Give an example of a number that is not real.

(the square root of any negative number)

(any number divided by zero)

300

Find a real number that's bigger than the square root of 81 and smaller than 3³

Any whole number, fraction, or decimal between 9 and 27

400

Real, rational, irrational, integer. Name all that apply for 2/7

irrational, real

.2857142... it will keep going on and on without any apparent pattern. That's why it's irrational. It is real because all rational and irrational numbers are real.

500

Find the square root of 9²

Now divide your answer by 4.

Real, rational, irrational, integer. Name all that apply to your answer. 

Answer should be 9/4, or 2 1/4, or 2.25. That number is real and rational because the decimal terminates.