Algebra I
9.2 Simplifying radicals
Goal 1 Simplifying radicals
Properties of radicals
Product property The square root of a product
equals the product of the square roots of the factors.
√ab = √a • √b where a ≥ 0 and b ≥ 0
Example √400 = √4 • 100 = √4 •√100
Quotient property The square root of a quotient
equals the quotient of the square roots of the
numerator and denominator.
a
√b =
√a
√b
where a ≥ 0 and b > 0
9
Example √25 =
√9
√25
Simplest form
No perfect square factors other than 1 are in the
radicand.
√8 = √2 • 4 = 2√2
No fractions are the radicand.
√
5
16
=
√5
√16
=
√5
4
No radicals appear in the denominator of a fraction
1
√4
=
1
2
Example 1 Simplifying with the product property
Simplify the expression √48
Example 2 Simplifying with the quotient property
Simplify the expression
7
a. √16
b.
√18
3
80
c. √45
Goal 2 Using quadratic models in real life
Example 3 Simplifying radical expressions
The distance d you can see to the horizon depends
on your height h. A model is d2=1.5h, with d in miles
and h in feet.
a. Find the exact distance you can see from the top
of a 400ft building.
b. Find the distance in Part(a) to the nearest tenth.
c. If you were 3 x 400 = 1200ft up in a skyscraper,
how far could you see to the nearest tenth?