Page 465 - Algebra 1

It is not always apparent that radicals are alike until they are simplified. All radicals should be simplified before trying to identify like radicals.
Simplifying Before Combining
Example
2
Simplify. All variables represent non-negative real numbers. 3
a. 3√ 8m + 2√ 2m + 4√ 2m SOLUTION
√ √ √ 3 8m3+2 2m+4 2m
Hint
Use the Product Property of Radicals. If a ≥ 0
and b ≥ 0, then √ ab = √ a • √ b .
√ √ √
=3 4·m2 ·2m +2 2m +4 2
2m
= 3√ 4 · √ m · √ 2m + 2√ 2m + 4√ 2m
Factor the first radicand.
= 6m√ 2m + 2√ 2m + 4√ 2m = ( 6 m + 2 + 4 ) √ 2 m
= ( 6 m + 6 ) √ 2 m
b. c√ 75 c-√ 27 c3 SOLUTION
c√ 75 c - √ 27 c3 =c√ 25·√ 3c-√ 9·√ c2 ·√ 3c = 5c√ 3c - 3c√ 3c
= (5c - 3c)√ 3c
= 2 c √ 3 c
Simplify 3√ 4 · √ m . Factor out √ 2m . Simplify.
Product Property of Radicals 2
Application: Finding the Perimeter of a Triangle
Factor the radicands. Simplify each expression. Factor out √ 3c.
Simplify.
Example
3
Find the perimeter of a right triangle if the lengths of the two legs are 4√9 inches and 2√6 4 inches, and the hypotenuse is 2√1 0 0 inches.
SOLUTION
The perimeter is the distance around the figure. P = 4√ 9 + 2√ 64 + 2√ 10 0
2 √64 in.
2 √100 in
450 Saxon Algebra 1
√ √ √ P=4 32+2 82+2 102
P = 4 · 3 + 2 · 8 + 2 · 10 P = 12 + 16 + 20
P = 48
The perimeter is 48 inches.
Factor each radicand. Simplify each radical. Multiply.
Add.
4 √9 in.