6.1 Properties of Square Roots

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:

More Examples:Simplify:

You Try!Simplify:

Using the Quotient PropertySimplify

Examples:Simplify:

You Try!Simplify:

Evaluating Square Roots1. Plug in given values for each

variable. USE PARENTHESES!!

2. Simplify under the radical sign.

3. Reduce/simplify the square root.

ExampleEvaluate when a = 2, b = -8, and c = 4.

ExampleEvaluate when a = 20 and

b = 16

You Try!Evaluate when a = 2, b = -6, and c = -5.

Simplifying Radical ExpressionsSimplify the radical (square root) first.

Then divide/reduce.Example:

Example:Simplify:

Example:Simplify:

Example:Simplify:

You Try!

Simplifying Variable ExpressionsFor 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