9.2 – Simplifying Radicals
Today we will be learning how to:
Use properties of radicals to simplify radicals
Use quadratic equations to model real-life
problems
Evaluate the radical expressions √ab and √a  √b for
the given values of a and b.
a = 4, b = 9
a = 25, b = 4
a = 36, b = 16
Evaluate the radical expressions
given values of a and b.
a = 4, b = 49
a = 16, b = 64
a = 144, b = 100

a
and
b
a
b
for the
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
Ex. √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
a

b
b
Ex.


where a ≥ 0 and b > 0
9
9

25
25
An expression is in simplest form if:
No perfect square factors other than 1 are in the radicand
√8 = √42 = 2√2
No fractions are in the radicand
5
5
5


16
4
16
No radicals appear in the denominator of a fraction

1
1

4 2

Example 1
Simplify the expression √48
Example 2
Simplify the expression
7
16

18
3

80
45

Example 3
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.
Find the exact distance you can see from the top of a 400 ft
building.
Example 3
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.
Find the distance in part 1 to the nearest tenth.
Example 3
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.
If you were 3 × 400 = 1200 ft up in a skyscraper, how far could you
see to the nearest tenth?
HOMEWORK
Page 514
#10 – 48 even