Page 114 - MarceAlgebra Demystified

CHAPTER 5 Exponents and Roots 101

Roots of fractions or fractions with a root in the denominator are not
p ffiffiffiffiffi
n
simplified. To eliminate roots in denominators, use the fact that n a ¼ a
and that any nonzero number over itself is one. We will begin with square
roots. If the denominator is a square root, multiply the fraction by the denomi-
nator over itself. This will force the new denominator to be a perfect square.

Examples

p ffiffiffi p ffiffiffi p ffiffiffi p p p
ffiffiffi
ffiffiffi
ffiffiffi
1 1 2 2 2 4 4 x 4 x 4 x
p ffiffiffi ¼ p p ¼ p ffiffiffiffiffi ¼ p ffiffiffi ¼ p p ¼ p ffiffiffiffiffi ¼
ffiffiffi
ffiffiffi
ffiffiffi
ffiffiffi
2 2 2 2 2 2 x x x x 2 x
p ffiffiffi p p p
r ffiffiffi ffiffiffi ffiffiffi ffiffiffi
2 2 3 6 6
¼ p p ¼ p ffiffiffiffiffi ¼
ffiffiffi
ffiffiffi
3 3 3 3 2 3
Practice
3
1: p ¼
ffiffiffi
5
7
2: p ¼
y
ffiffiffi
r ffiffiffi
6
3: ¼
7
8x
4: p ¼
ffiffiffi
3
r ffiffiffiffiffiffiffiffi
7xy
5: ¼
11

Solutions
p ffiffiffi p ffiffiffi p ffiffiffi
3 3 5 3 5 3 5
1: p ¼ p p ¼ p ffiffiffiffiffi ¼
ffiffiffi
ffiffiffi
ffiffiffi
5 5 5 5 2 5
p p p
7 7 y 7 y 7 y
ffiffiffi
ffiffiffi
ffiffiffi
ffiffiffiffiffi ¼
y y y y 2 y
2: p ¼ p p ¼ p
ffiffiffi
ffiffiffi
ffiffiffi