7.2 simplifying radicals
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7.2 Simplifying Radicals
Square Root VocabThe square root symbol is called a “radical sign”
The number inside is the “radicand”
Properties:Product Property
Quotient Property
Simplifying Square RootsA square root is simplified when the radicand has no perfect square factors (other than 1).
Method 1:Use Product Property to rewrite using largest perfect square factor.
SimplifyExample:
Method 2:Make a factor tree.Any number that “finds a date” gets to go outside the radical.
Example:
Examples:Simplify:
You Try!Simplify:
Using the Quotient Property
Simplify
Examples:Simplify:
You Try!Simplify:
Simplifying Variable Expressions
For expressions like this:Simplify the number part as usual.
Pairs of each variable go outside.
Example:Simplify
Example:Simplify
Example:Simplify
You Try!Simplify:
Example:Simplify
Example:Simplify
You Try!Simplify
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
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
Finding nth RootsSimplify each expression:
Examples:Simplify:
You Try!Simplify:
Simplify:
More Simplifying
Simplify:
You Try!
Simplify:
Simplifying Variable Expressions
Simplify:
Simplify:
You Try!