Page 415 - Algebra 1

Simplifying With Powers of Ten
Simplify using powers of ten.
a. √ 10 ,00 0
SOLUTION Write the radicand as a power of ten. Then simplify.
Write the radicand as a power of ten. Find factors that are perfect squares. Product Property of Radicals Simplify.
Multiply.
b. √ 100 ,0 00
SOLUTION Write the radicand as a power of ten. Then simplify.
Write the radicand as a power of ten. Find factors that are perfect squares. Product Property of Radicals
S i m p l i f y .
Multiply.
The rules of radicals and exponents apply to variable expressions.
Simplifying With Variables
Simplify. All variables represent non-negative real numbers.
SOLUTION Use the Product Property of Radicals. Then simplify.
Product Property of Radicals Simplify.
Multiply.
b. 162r4s8
SOLUTION Use the Product Property of Exponents
Example
3
√1 0 ,00 0 4
= √1 0 22
= √1 0 · 1 0 22
= √1 0 · √1 0 = 10 · 10
= 100
Math Reasoning
Generalize Find a pattern in the square roots of powers of ten.
√1 00 ,0 00 5
= √1 0 221
= √1 0 · 1 0 · 1 0 221
= √1 0 · √1 0 · √1 0 = 1 0 · 1 0 · √ 1 0
= 100 √1 0
Example
4
a. √81xy
43
43
√81x y
43 = √8 1 · √x · √y
=9·x2 ·y √y = 9x2y√y
48 = √ 1 6 2 r s
48 = √1 6 2 · √r · √s
2244 = √8 1 · √2 · √r · √r · √s · √s
= 9 · √2 · r2 · s4 = 9r2s4 √2
400 Saxon Algebra 1
√
Product Property of Radicals
Find factors that are perfect squares. Simplify.
Multiply.