Including Rationalizing The Denominators

Warm Up Simplify each expression

Multiply and divide radical expressions. Rationalize denominators. Objectives You can use the Product and Quotient Properties of square roots you have already learned to multiply and divide expressions containing square roots.

Multiplying Square Roots Multiply. Write the product in simplest form. Product Property of Square Roots. Multiply the factors in the radicand. Factor 16 using a perfect-square factor. Product Property of Square Roots Simplify. COPY

Multiplying Square Roots Multiply. Write the product in simplest form. Expand the expression. Commutative Property of Multiplication. Product Property of Square Roots. Simplify the radicand. Simplify the Square Root. Multiply. COPY

Multiplying Square Roots Multiply. Write the product in simplest form. Product Property of Square Roots. Factor 4 using a perfect-square factor. Take the square root.. Simplify. COPY

Try This! Multiply. Write the product in simplest form. Product Property of Square Roots. Multiply the factors in the radicand. Factor 25 using a perfect-square factor. Product Property of Square Roots Simplify.

Try This! Multiply. Write the product in simplest form. Expand the expression. Commutative Property of Multiplication. Product Property of Square Roots. Simplify the radicand. Simplify the Square Root. Multiply.

Try This! Multiply. Write the product in simplest form. Product Property of Square Roots. Factor 14 using a perfect-square factor. Take the square root. Simplify.

Using the Distributive Property Multiply. Write each product in simplest form. Product Property of Square Roots. Multiply the factors in the second radicand. Factor 24 using a perfect-square factor. Product Property of Square Roots. Simplify. Distribute COPY

Using the Distributive Property Multiply. Write the product in simplest form. Product Property of Square Roots. Distribute Simplify the radicands. Simplify.

Try This! Multiply. Write the product in simplest form. Product Property of Square Roots. Multiply the factors in the first radicand. Factor 48 using a perfect-square factor. Product Property of Square Roots. Simplify. Distribute

Try This! Multiply. Write the product in simplest form. Product Property of Square Roots. Simplify the radicand. Simplify. Distribute COPY

Try This! Multiply. Write the product in simplest form. Product Property of Square Roots. Simplify the radicand. Simplify. Distribute

Try This! Multiply. Write each product in simplest form. Product Property of Square Roots. Simplify the radicand. Simplify. Distribute

A quotient with a square root in the denominator is not simplified. To simplify these expressions, multiply by a form of 1 to get a perfect-square radicand in the denominator. This is called rationalizing the denominator.

Rationalizing the Denominator Simplify the quotient. Multiply by a form of 1 to get a perfect-square radicand in the denominator. Product Property of Square Roots. Simplify the denominator. COPY

Rationalizing the Denominator Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator. COPY

Try This! Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator.

Try This! Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator. COPY

Try This! Simplify the quotient. Simplify the square root in denominator. Multiply by a form of 1 to get a perfect- square radicand in the denominator. Factor and simplify the square root in the numerator. COPY

Lesson Quiz Multiply. Write each product in simplest form Simplify each quotient