Exponents, Roots, and Irrationals Review

Scientific Notation

100

Change 0.00043 into scientific notation.

4.3 x 10^-4

200

Convert this into standard form.

5.6 x 10⁶

5,600,000 (5.6 million)

300

(2.9 x 10³)+(3.1 x 10⁵)

3.129 x 10⁵

400

(8.3 x 10³)(6.2 x 10^-2)

5.146 x 10²

500

(0.98 x 10^-2)/(0.5 x 10¹)

1.96 x 10^-3

Exponents

100

(3x²y⁴)(-9x^-4y)

-27y⁵/x²

200

(4x²y³)²

16x⁴y⁶

300

(5x^-2y⁴)³

125y¹²/x⁶

400

12x³y^-4/4x^-4y⁶

3x⁷/y¹⁰

500

(4x³)(5x^-2)/15x³

4/3x²

Square Roots

100

What is the square root of 81?

9

200

What is the decimal for the square root of 79?

8.8 or 8.9

300

What is the decimal for the square root of 35?

5.9

400

Simplify square root of 125

5 times the square root of 5

500

Simplify square root of 180

6 times the square root of 5.

Rational vs. Irrational

100

Is -8 rational or irrational? why?

It is rational because its decimal -8.0 terminates or ends.

200

Is pi rational or irrational? why?

Pi is irrational because it is a decimal that never ends and has no pattern of numbers.

300

Is is the square root of 2 rational or irrational? why?

It is irrational because it is not a perfect square. It is a decimal that never ends. And doesn't have a pattern.

400

-1 is a rational number. What other classifications can you give it?

integer, rational, real.

500

the square root of 121 is 11. What are some classifications for the number 11?

real, natural, whole, integer, and rational.

Solving with square roots

100

5x²+45=95

plus and minus square root of 10

200

6x²-54=24

plus and minus the square root of 13.

300

-12x²+64=-100

plus and minus the square root of 3.

400

1/3x²+12=24

plus and minus 6

500

1/3x²-16=28

plus and minus the square root of 132 OR 2 times the square root of 33.