Algebra Demystified 2nd Ed

Chapter 10 QuadratiC EQuations 367

Simplifying this expression is much easier than the expression containing
all of the fractions.

Sometimes we must simplify the solutions we find with the quadratic for-
mula. We begin by simplifying the square root if the number under the
radical has a perfect square as a factor. For example, 12 is not simplified
because 12 has 4, a perfect square, as a factor. We simplify 12 with the
radical properties ab =  ab⋅ and aa^2  =  (provided a and b are not
negative). Thus we obtain 12   =  43 ⋅⋅=  43  =  23.

Once we simplify the square root, we then see if the numerator and denom-
inator have any common factors. If so, we factor the numerator and divide
out the common factor.

EXAMPLES
Simplify the fraction.

824

2

±

We begin by simplifying the square root: 24   =  46 ⋅ 26 = 

824

2

826

2

± = ±

The denominator is divisible by 2 and each term in the numerator is divis-
ible by 2, so we factor a 2 from each term in the numerator. We then divide
2 from the numerator and denominator.

826

2

24 6

2

± = ()± =± 46

Simplify the fractions.

−± (^318) =−± ⋅ =−± = −± =−±
6
392
6
332
6
31 2
6
12
2
()
15 50
10
15 252
10
15 52
10
53 2
10
32
2
± = ±⋅= ± = ()± = ±
EXAMPLES
Simplify the fraction.
EXAMPLES
Simplify the fraction.