Page 144 - Math Course 2 (Book 1)

Simplifying Radical Expressions

Mo. 5

Lesson 1 Key Concept

Product Property of
KEY CONCEPTS: Square Roots
1. Simplify radical expression using the
Product Property of Square Roots. Words For any numbers a and b, where a > 0
and b > 0, the square root of the product
2. Simplify radical expression using the ab is equal to the product of each
Quotient Property of Square Roots. square root.

Symbols ab = a • b
MO. 5 - L1a

Product Property of Square Example 4 • 25 = 4 • 25
Roots

Vocabulary A-Z Concept Summary

Let us learn some vocabulary Simplest Radical Form

A radical expression is in simplest form when the
following three conditions have been met.
Radical expression
1. No radicand have perfect square factors other
than 1.
A radical expression is an expression that contains a
square root. 2. No radicand contain fraction.
3. No radicals appear in the denominator of a
3 –2 2GM fraction.
(–3) 5 R
X

Radicand
Let’s Begin
A radicand is the expression under the radical sign.

Radical Sign 137xy 2 Radicand Simplify Square Roots

Example

Conjugate

p q –r s
Binomials of the form and Simplify 52
p q + r s
are called conjugates. Conjugates are useful when 52 = 2 • 2 • 13 Prime factorization of 52.
simplifying radical expressions because if p, q, r,
and s are rational numbers, the product of the two = 2 2 • 13 Product Property of Square
conjugates is a rational number Roots.

2
(a – 2)(a + 2) = a + 2 = 2 • 13 Simplify.
2
(3 + 2)(3 – 2) = 3 – ( 2 ) 2 a = 3, b = 2
= 9 – 2 or 7 ( 2 ) = 2 • 2 or 2 Answer 2 13

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