Simplify Radical Expressions

EQs…  How do we simplify algebraic and numeric expressions involving square root?  How do we perform operations with square roots?

Vocabulary  Simplest Form – A radical expression is in simplest form if no perfect square factors other than 1 are in the radicand, no fractions are in the radicand, and no radicals appear in the denominator of the fraction.  Rationalizing the Denominator – The process of eliminating a radical from an expression’s denominator.

Vocabulary  Radical Conjugates –  Product Property of Radicals – States that the square root of a product equals the product of the square roots of the factors.  Quotient Property of Radicals – States that the square roots of a quotient equals the quotient of the square roots of the numerator and denominator.

Example 1 Use the product property of radicals  Simplify the expression.

Example 2 Multiply radicals  Simplify the expression.

Example 3 Use the quotient property of radicals  Simplify the expression.

Guided Practice for Examples 1, 2, & 3  Simplify the expression.

Guided Practice for Examples 1, 2, & 3  Simplify the expression.

Example 4 Rationalize the denominator

Example 5 Add and Subtract Radicals

Guided Practice for Examples 4 & 5 Add and Subtract Radicals

Joke of the Day…  Why was the math book crying?

 It had too many problems!