Algebra Chapter 1

Squares & Square Roots

100

What is a perfect square?

A number that has a whole number as its root.

200

What are the square roots of 9?

+3 & -3

300

Evaluate the expression:

2² + 17

21

400

Solve for x:

x² - 18 = 82

x= 10, -10

500

Solve for x: 

3x² - 8 =184

x = 8, -8

Pythagorean Theorem & Converse

100

What is Pythagorean Theorem?

a² + b² = c²

200

What is the converse of Pythagorean Theorem?

If a² + b² = c², it is a right triangle.

300

A right triangle has a height of 24 in. and a length of 10 in. What is the length of the hypotenuse?

26 inches

400

Is this a right triangle?

8, 9, 12

No. 64 + 81 does not equal 144.

500

A right triangle has a hypotenuse of 25 yd. and a height of 24 yd. What is the length of the third side?

7 yd.

Cubes & Cube Roots

100

What is a perfect cube?

A number that has a whole number as its cube root?

200

What is the cube root of 8?

2

300

Evaluate the expression:

5³ - 22

103

400

Solve for x:

x³ + 14 = 743

x = 9

500

Solve for x (leave answer in the radical):

4x³ - 6 = 92

x = cube root of 24.5

Decimals & Fractions

100

Is 1/2 a decimal? Explain.

No, it doesn't have a decimal point (it's a fraction).

200

Is 1/6 a fraction? Explain.

Yes, it has a numerator & denominator?

300

Write .8282... as a fraction.

82/99

400

Write 6/11 as a decimal. 

.54...

500

Compare: 5/13 & .6565...

Have both numbers written as a decimal & compare using < , > , or =.

.385 < .6565...

Rational & Irrational Numbers

100

What is a rational number?

A number that can be written as a fraction.

200

What is an irrational number?

A number that can't be written as a fraction.

300

Is 7/8 rational? Explain.

Yes, it's written as a fraction.

400

Is .8787... rational? Explain.

Yes, repeating decimals can be written as fractions.

500

Is (-16)^1/2 rational? Explain.

No, square roots of negative numbers are irrational.