Page 108 - MarceAlgebra Demystified

CHAPTER 5 Exponents and Roots 95

2x
4: ¼
ð3yÞ 2

2x 3
5: ¼
2x þ 5

Solutions

4x 2
2 5
1: ¼ 4x y
y 5
2xðx 3Þ
2: ¼ 2xðx 3Þðx þ 1Þ 2
ðx þ 1Þ 2
x
3: ¼ xy 1
y

2x
4: ¼ 2xð3yÞ 2
ð3yÞ 2

2x 3
5: ¼ð2x 3Þð2x þ 5Þ 1
2x þ 5

Roots

The square root of a number is the nonnegative number whose square is the
2
root. For example 3 is the square root of 9 because 3 ¼ 9.

Examples
p ffiffiffiffiffi 2 p ffiffiffiffiffi 2
16 ¼ 4 because 4 ¼ 16 81 ¼ 9 because 9 ¼ 81
p ffiffiffiffiffiffiffiffi 2
625 ¼ 25 because 25 ¼ 625
It may seem that negative numbers could be square roots. It is true that
p
2
9 is the symbol for the nonnegative number whose
ð 3Þ ¼ 9. But ffiffiffi
square is 9. Sometimes we say that 3 is the principal square root of 9.
When we speak of an even root, we mean the nonnegative root. In