Adding
Addingand
andSubtracting
Subtracting
11-7Radical
11-7
RadicalExpressions
Expressions
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Algebra
Holt
Algebra
11
Adding and Subtracting
11-7 Radical Expressions
Warm Up
Simplify each expression.
1. 14x + 15y – 12y + x 15x + 3y
2. 9xy + 2xy – 8xy 3xy
3. –3(a + b) +
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–3a – b + 10
Adding and Subtracting
11-7 Radical Expressions
Warm Up Continued
Simplify. All variables represent
nonnegative numbers.
4.
5.
6.
Holt Algebra 1
Adding and Subtracting
11-7 Radical Expressions
Objective
Add and subtract radical expressions.
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Adding and Subtracting
11-7 Radical Expressions
Vocabulary
like radicals
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Adding and Subtracting
11-7 Radical Expressions
Square-root expressions with the same radicand are
examples of like radicals.
Holt Algebra 1
Adding and Subtracting
11-7 Radical Expressions
Like radicals can be combined by adding or subtracting.
You can use the Distributive Property to show how this
is done:
Notice that you can combine like radicals by adding or
subtracting the numbers multiplied by the radical and
keeping the radical the same.
Holt Algebra 1
Adding and Subtracting
11-7 Radical Expressions
Helpful Hint
Combining like radicals is similar to combining
like terms.
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Adding and Subtracting
11-7 Radical Expressions
Example 1: Adding and Subtracting Square-Root
Expressions
Add or subtract.
A.
The terms are like radicals.
B.
The terms are unlike radicals. Do
not combine.
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Adding and Subtracting
11-7 Radical Expressions
Example 1: Adding and Subtracting Square-Root
Expressions
Add or subtract.
C.
the terms are
like radicals.
D.
Identify like radicals.
Combine like radicals.
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Adding and Subtracting
11-7 Radical Expressions
Check It Out! Example 1
Add or subtract.
a.
The terms are like radicals.
b.
The terms are like radicals.
Holt Algebra 1
Adding and Subtracting
11-7 Radical Expressions
Check It Out! Example 1
Add or subtract.
c.
The terms are like radicals.
d.
The terms are like
radicals.
Combine like radicals.
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Adding and Subtracting
11-7 Radical Expressions
Sometimes radicals do not appear to be like
until they are simplified, Simplify all radicals in
an expression before trying to identify like
radicals.
Holt Algebra 1
Adding and Subtracting
11-7 Radical Expressions
Example 2A: Simplify Before Adding or Subtracting
Simplify each expression.
Factor the radicands using perfect
squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.
Holt Algebra 1
Adding and Subtracting
11-7 Radical Expressions
Example 2B: Simplify Before Adding or Subtracting
Simplify each expression.
Factor the radicands using perfect
squares.
Product Property of Square Roots.
Simplify.
The terms are unlike radicals. Do
not combine.
Holt Algebra 1
Adding and Subtracting
11-7 Radical Expressions
Example 2C: Simplify Before Adding or Subtracting
Simplify each expression.
Factor the radicands
using perfect squares.
Product Property of
Square Roots.
Simplify.
Combine like radicals.
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Adding and Subtracting
11-7 Radical Expressions
Remember!
When you write a radicand as a product, make at
least one factor a perfect square.
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Adding and Subtracting
11-7 Radical Expressions
Check It Out! Example 2a
Simplify each expression.
Factor the radicands using perfect
squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.
Holt Algebra 1
Adding and Subtracting
11-7 Radical Expressions
Check It Out! Example 2b
Simplify each expression.
Factor the radicands using perfect
squares.
Product Property of Square Roots.
Simplify.
The terms are unlike radicals. Do not
combine.
Holt Algebra 1
Adding and Subtracting
11-7 Radical Expressions
Check It Out! Example 2c
Simplify each expression.
Factor the radicands using perfect
squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.
Holt Algebra 1
Adding and Subtracting
11-7 Radical Expressions
Example 3: Geometry Application
Find the perimeter of the
triangle. Give the answer
as a radical expression in
simplest form.
Write an expression for perimeter.
Factor 20 using a perfect square.
Product Property of Square Roots.
Simplify.
Combine like radicals.
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Adding and Subtracting
11-7 Radical Expressions
Check It Out! Example 3
Find the perimeter of a rectangle whose length
is
inches and whose width is
inches.
Give your answer as a radical expression in
simplest form.
Write an expression for perimeter
2 (l + w).
Multiply each term by 2 .
Simplify.
Combine like radicals.
The perimeter is
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in.
Adding and Subtracting
11-7 Radical Expressions
Lesson Quiz: Part I
Add or subtract.
1.
2.
3.
Simplify each expression.
4.
5.
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Adding and Subtracting
11-7 Radical Expressions
Lesson Quiz: Part II
6. Find the perimeter of the trapezoid. Give the
answer as a radical expression is simplest form.
Holt Algebra 1