# Chapter 11 Section 3

Preview
Warm Up
California Standards
Lesson Presentation
Warm Up
Simplify each expression.
1. 14x + 15y – 12y + x
15x + 3y
2. 9xy + 2xy – 8xy 3xy
3. –3(a + b) +
–3a – b + 10
Simplify. All variables represent nonnegative
numbers.
4.
5.
6.
California
Standards
Extension of
2.0
Students understand and use such operations
as taking the opposite, finding the reciprocal,
taking a root, and raising to a fractional power.
They understand and use the rules of exponents.
Vocabulary
Square-root expressions with the same radicand are
subtracting. You can use the Distributive Property to
show how this is done:
subtracting the numbers multiplied by the radical and
Combining like radicals is similar to combining
like terms.
Square-Root Expressions
A.
B.
The terms are unlike radicals. Do
not combine.
Square-Root Expressions
C.
the terms are
D.
Check It Out! Example 1
a.
b.
Check It Out! Example 1
c.
d.
Sometimes radicals do not appear to be like
until they are simplified. Simplify all radicals in
an expression before trying to identify like
Subtracting
Simplify each expression. All variables
represent nonnegative numbers.
squares.
Product Property of Square Roots
Simplify.
Subtracting
Simplify each expression. All variables
represent nonnegative numbers.
squares.
Product Property of Square Roots
Simplify.
The terms are unlike radicals. Do
not combine.
Subtracting
Simplify each expression. All variables
represent nonnegative numbers.
using perfect squares.
Product Property of
Square Roots
Simplify.
Remember!
When you write a radicand as a product, make at
least one factor a perfect square.
Check It Out! Example 2a
Simplify each expression. All variables
represent nonnegative numbers.
squares.
Product Property of Square Roots
Simplify.
Check It Out! Example 2b
Simplify each expression. All variables
represent nonnegative numbers.
squares.
Product Property of Square Roots
Simplify.
The terms are unlike radicals. Do not
combine.
Check It Out! Example 2c
Simplify each expression. All variables
represent nonnegative numbers.
squares.
Product Property of Square Roots
Simplify.
Find the perimeter of the
simplest form.
Write an expression for perimeter.
Factor 20 using a perfect square.
Product Property of Square Roots
Simplify.
Check It Out! Example 3
Find the perimeter of a rectangle whose length
is
inches and whose width is
inches.
simplest form.
Write an expression for perimeter
2 (l + w).
Multiply each term by 2 .
Simplify.
The perimeter is
in.
Lesson Quiz: Part I