Page 414 - Algebra 1

Exploration Finding Products of Square Roots
If a is equal to the area of a square, then √a is the length of a side of the
square. The formula for the area of a square is side length × side length,
which can be written as √a · √a = a.
a. Use the formula for the area of a square to write the area of a square that is 4 units squared.
b. Simplify the formula for the area of a square that is 4 units2 using the Product of Radicals Rule.
c. Simplify the product formed by the radicand.
d. Verify Find the square root to show whether the equation is true.
The product of the square root of the area and the square root of the same area is equal to the area. This rule can be applied to all non-negative real numbers.
e. Generalize Write a rule for simplifying the expression √x · √x, where x
is a non-negative real number.
f. Simplify √ 4 · √ 4 using the Product of Radicals Rule.
g. Simplify the radicand using the Product Property of Exponents.
h. Generalize Write a rule for simplifying the expression √ x2, where x is a
non-negative real number.
Another way to simplify radical expressions is by factoring the radicand into prime numbers.
Simplifying With Prime Factors
Simplify using prime factorization. √1 8 0
Example
2
SOLUTION
√1 8 0
= √2 · 2 · 3 · 3 · 5
= √2 · √2 · √3 · √3 · √5 = 2 · 3 √5
= 6 √ 5
Find the prime factorization. Product Property of Radicals Simplify.
M u l t i p l y .
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