Page 146 - Math Course 2 (Book 1)

Simplifying Radical Expressions

MO. 5 - L1b Key Concept

Quotient Property of Square Quotient Property of

Roots Square Roots

Words For any numbers a and b, where
Vocabulary A-Z a > 0 and b > 0, the square root of the
a
Let us learn some vocabulary quotient is equal to the quotient
b
of each square root.

Symbols a = a
Rationalizing the Denominator b b

Rationalizing the denominator of a radical expression Example 49 = 49
4
is a method used to eliminate radicals from a 4
denominator.
Concept Summary

10 10 Quotient Property Simplest Radical Form
3 = 3 of Square Roots
A radical expression is in simplest form when the
10 • 3 3 following three conditions have been met.
= Multiply by
3 • 3 3
1. No radicands have perfect factors other than 1.
30 Product Property 2. No radicands contain fraction.
= 3. No radicals appear in the denominator of a
3 of Square Roots
fraction.

Let’s Begin

Rationalizing the Denominator Simplify 3n
8

Examples 3n = 3n • 8 Multiply by 8
8 8 8 8
12 24n Product Property of
Simplify =
5 8 Square Roots

2•2•2•3n Prime factorization
12 = 12 • 5 Multiply by 5 =
5 5 5 5 8

Product Property of = 2 6n 2 2 = 2
= 60 Square Roots 8
5
6n Divide the numerator and
2 15 =
= Simplify. 4 denominator by 2.
5
2 15 6n
Answer Answer
5 4

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