Simplifying Radical Expressions

Chapter 10 Section 1Kalie Stallard

• Radical Expression: an expression that contains a square root. Ex:

• Radicand: The expression under the square root sign.

• Expression is in Simplest Form when the radicand contains no perfect square factors other than 1. – Is in simplest form?– Is 3 in simplest form?

Product Property of Square Roots

• The square root of the product ab is equal to the product of each square root. a and b both have to be ≥ 0

Example:

Product Property of Square RootsSimplify the Following

•

• 3

Product Property of Square RootsSimplify the Following

• 3

Simplify a Square Root with Variables

• When finding the square root of an expression containing variables, be sure that the result is not negative.

• = │x│ Let’s look at x=-2

Quotient Property of Square Roots

• The square root of is equal to each square root a and b. a and b both have to be ≥ 0

Example:

Quotient Property of Square Roots

Rationalizing the Denominator of a radical expression is a method used to eliminate radicals from a denominator.

• Multiply by

Rationalizing the Denominator

• • Multiply by

Concept Summary

• A radical expression is in simplest form when the following three conditions have been met.

1. No radicands have perfect square factors other than 1.

2. No radicands contain fractions3. No radicals appear in the denominator of a

fraction.

Homework

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