Radical operations

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Radical operations
Vocabulary
radical expression radicand index rationalize extr
aneous solutions
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Radical Notation
Square Root Notation
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Simplifying Radical Expressions.
Examples of radical expressions
The expression under a radical sign is the
radicand. A radicand may contain numbers,
variables, or both. It may contain one term or
more than one term.
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Simplifying Radical Expressions

• An expression containing a radical is in simplest
  form when
• the radicand has no perfect square factors
  other than 1.
• the radicand has no fractions
• there are no radicals in any denominator

Examples of non-simplified radical expressions
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Simplifying Radical Expressions

• A Square number is 16
• The Squared number is 4 which results in or
  16
• What happens to a squared number when you find
  its square root ?
• Evaluate

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• Simplifying Radical Expressions
• Product Quotient Property

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Objective
Add and subtract radical expressions.
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Vocabulary
like radicals
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Square-root expressions with the same radicand
are examples of like radicals.
Combining like radicals is similar to combining
like terms.
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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.
The terms are like radicals.
D.
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Simplify all radicals in an expression before
trying to identify like radicals. (Sometimes
radicals do not appear to be like until they are
simplified.)
Example 1 Simplify Before Adding or Subtracting
Simplify the expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.
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A quotient with a square root in the denominator
is not simplified. To simplify these expressions,
multiply by a form of 1 to get a perfect-square
radicand in the denominator. This is called
rationalizing the denominator.
Simplify the quotient.
Multiply by a form of 1 to get a perfect-square
radicand in the denominator.
Product Property of Square Roots.
Simplify the denominator.
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Multiplying and Dividing Radical Expressions
You can use the Product and Quotient Properties
of square roots you have already learned to
multiply and divide expressions containing square
roots.
Example Multiply and Simplify
Product Property of Square Roots.
Multiply the factors in the radicand.
Factor 16 using a perfect-square factor.
Product Property of Square Roots
Simplify.
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Example 1 Using the Distributive Property
Multiply. Write the product in simplest form.
Product Property of Square Roots.
Simplify the radicands.
Simplify.
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Example 2 Using the Distributive Property
Multiply. Write the product in simplest form.
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Solving Simple Radical Equations
Solve the equation. Check your answer.
Square both sides.
x 25
Substitute 25 for x in the original equation.
?
Simplify.
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Example Extraneous Solutions
Solve Check your answer.
Subtract 12 from each sides.
Square both sides
6x 36
Divide both sides by 6.
x 6
Substitute 6 for x in the equation.
?
18 6
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Solving Radical Equations by Multiplying or
Dividing
Solve the equation. Check your answer.
Method 1
Multiply both sides by 2.
Square both sides.
144 x