Chapter 5.1 - Roots & Rational Exponents

√25 = ±5

Why?

Because 5 × 5 = 25

√-25 = ±5i …

or no real roots

3√216 = 6

Why?

B/c 6 × 6 × 6 = 216

3√-216 = -6

Why?

B/c -6 x -6 x -6 = -216

Cubic root doesn’t need a…

± (plus or minus sign)

n√A.. (names of n and A)

n = root

A = radicand

n is EVEN and A is POSITIVE…

± real number

n is ODD and A is POSITIVE…

positive (+) real number

n is EVEN and A is NEGATIVE…

no real numbers

n is ODD and A is NEGATIVE…

negative (-) real number

5² = 25

25^? = 5

½ because..

2 × ½ = 1, therefore..

(5²)^1/2 = 5

5^{2 × 1/2} = 5

5¹ = 5

1⁵ =

1

2⁵ =

32

3⁵ =

243

4⁵

5⁵ =

3,125

6⁵ =

7,776

7⁵ =

16,807

8⁵ =

32,768

9⁵ =

59,049

10⁵ =

100,000