Simplify Radical Expressions What steps would you take in simplifying the following: √(3+92)

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.

Multiplying Radicals * To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

Multiply and then simplify

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

+ To combine radicals: combine the coefficients of like radicals Combining Radicals + To combine radicals: combine the coefficients of like radicals

Simplify each expression

Simplify each expression: Simplify each radical first and then combine.

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!