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!