Simplifying Radical

Expressions

Introduction to Square Roots

Warm Up:

Simplify the following:

Objective:

The student will be able to simplify radicals and rationalize a denominator

Think, Pair, Share:

What does it mean to have a root and how does this apply to Mathematics? If we can raise a number to a power is there some way we can “undo” it, if so how if not why not?

Simplest Radical Form

A radical expression is in its simplest form when the following three conditions have been met:

No radicands have perfect square factors other than 1.

No radicands contain fractions.

No radicands appear in the denominator of a fraction.

Product Property of Square Roots

Note

For radical expressions where the exponent of the variable inside the radical is even and the resulting exponent is odd, you must use the absolute value to ensure nonnegative results.

Ex:

Simplify a Square Root With Variables

With a Partner…

Quotient Property of Square Roots

Rationalizing the Denominator

With a Partner…

Simplify:

On Your Own…

Simplify:

Exit Ticket and Homework

Exit Ticket:

Simplify:

Homework:

Worksheet