7.2 simplifying radicals
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7.2 Simplifying Radicals
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Square Root VocabThe square root symbol is called a “radical sign”
The number inside is the “radicand”
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Properties:Product Property
Quotient Property
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Simplifying Square RootsA square root is simplified when the radicand has no perfect square factors (other than 1).
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Method 1:Use Product Property to rewrite using largest perfect square factor.
SimplifyExample:
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Method 2:Make a factor tree.Any number that “finds a date” gets to go outside the radical.
Example:
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Examples:Simplify:
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You Try!Simplify:
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Using the Quotient Property
Simplify
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Examples:Simplify:
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You Try!Simplify:
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Simplifying Variable Expressions
For expressions like this:Simplify the number part as usual.
Pairs of each variable go outside.
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Example:Simplify
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Example:Simplify
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Example:Simplify
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You Try!Simplify:
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Example:Simplify
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Example:Simplify
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You Try!Simplify
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What is an “nth Root?”Extends the concept of square roots.For example:A cube root of 8 is 2, since 23 = 8
A fourth root of 81 is 3, since 34 = 81
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For integers n greater than 1:if bn = a then “b is an nth root of a.” Written n is the index of the radical
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Finding nth RootsSimplify each expression:
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Examples:Simplify:
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You Try!Simplify:
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Simplify:
More Simplifying
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Simplify:
You Try!
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Simplify:
Simplifying Variable Expressions
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Simplify:
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Simplify:
You Try!