Adding and Subtracting Radical Expressions

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Adding and Subtracting Radical Expressions
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Objective
Add and subtract radical expressions.
Vocabulary
like radicals
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Square-root expressions with the same radicand
are examples of like radicals.
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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.
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Adding and Subtracting Square-Root Expressions
Add or subtract.
The terms are like radicals.
B.
The terms are unlike radicals. Do not combine.
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Adding and Subtracting Square-Root Expressions
Add or subtract.
C.
D.
Identify like radicals.
Combine like radicals.
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Try This!
Add or subtract.
The terms are like radicals.
The terms are like radicals.
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Try This!
Add or subtract.
c.
The terms are like radicals.
d.
Combine like radicals.
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Sometimes radicals do not appear to be like until
they are simplified, Simplify all radicals in an
expression before trying to identify like
radicals.
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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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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.
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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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Try This!
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.
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Try This!
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
The terms are unlike radicals. Do not combine.
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Try This!
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.
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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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Try This!
Write an expression for perimeter 2 (l w).
Multiply each term by 2 .
Simplify.
Combine like radicals.
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Lesson Quiz Part I
Add or subtract.
1.
2.
3.
Simplify each expression.
4.
5.
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Lesson Quiz Part II
6. Find the perimeter of the trapezoid. Give the
answer as a radical expression is simplest form.