Multiplying
Multiplyingand
andDividing
Dividing
11-8Radical
11-8
Radial Expressions
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Algebra
Holt
Algebra
11
Multiplying and Dividing
11-8 Radical Expressions
Warm Up
Simplify each expression.
1.
2.
3.
4.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Objectives
Multiply and divide radical
expressions.
Rationalize denominators.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
You can use the Product and Quotient Properties
of square roots you have already learned to
multiply and divide expressions containing square
roots.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Example 1A: 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.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Example 1B: 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.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Example 1C: Multiplying Square Roots
Multiply. Write the product in simplest form.
Factor 12 using a perfect-square factor.
Product Property of Square Roots.
Take the square root..
Simplify.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 1a
Multiply. Write the product in simplest form.
Product Property of Square Roots.
Multiply the factors in the radicand.
Factor 50 using a perfect-square factor.
Product Property of Square Roots
Simplify.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 1b
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.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 1c
Multiply. Write the product in simplest form.
Factor 14 using a perfect-square factor.
Product Property of Square Roots.
Take the square root.
Simplify.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Example 2A: Using the Distributive Property
Multiply. Write each product in simplest form.
Distribute
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.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Example 2B: Using the Distributive Property
Multiply. Write the product in simplest form.
Distribute
Product Property of Square Roots.
Simplify the radicands.
Simplify.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 2a
Multiply. Write the product in simplest form.
Distribute
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.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 2b
Multiply. Write the product in simplest form.
Distribute
Product Property of Square Roots.
Simplify the radicand.
Simplify.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 2c
Multiply. Write the product in simplest form.
Distribute
Product Property of Square Roots.
Simplify the radicand.
Simplify.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 2d
Multiply. Write each product in simplest form.
Distribute
Product Property of Square Roots.
Simplify the radicand.
Simplify.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
In Chapter 7, you learned to multiply binomials by
using the FOIL method. The same method can be
used to multiply square-root expressions that
contain two terms.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Remember!
First terms
Outer terms
Inner terms
Last terms
See Lesson 7-7.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
= 20
Holt Algebra 1
+3
Multiplying and Dividing
11-8 Radical Expressions
Example 3A: Multiplying Sums and Differences of
Radicals
Multiply. Write the product in simplest form.
Use the FOIL method.
Simplify by combining like terms.
Simplify the radicand.
Simplify.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Example 3B: Multiplying Sums and Differences of
Radicals
Multiply. Write the product in simplest form.
Expand the expression.
Use the FOIL method.
Simplify by combining like terms.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 3a
Multiply. Write the product in simplest form.
Use the FOIL method.
Simplify by combining like terms.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 3b
Multiply. Write the product in simplest form.
Expand the expression.
Use the FOIL method.
Simplify by combining like terms.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 3c
Multiply. Write the product in simplest form.
Expand the expression.
Use the FOIL method.
Simplify by combining like terms.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 3d
Multiply. Write the product in simplest form.
Use the FOIL method.
Simplify by combining like terms.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
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.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Example 4A: Rationalizing the Denominator
Simplify the quotient.
Multiply by a form of 1 to get a perfectsquare radicand in the denominator.
Product Property of Square Roots.
Simplify the denominator.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Example 4B: Rationalizing the Denominator
Simplify the quotient.
Multiply by a form of 1 to get a perfectsquare radicand in the denominator.
Simplify the square root in denominator.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 4a
Simplify the quotient.
Multiply by a form of 1 to get a perfectsquare radicand in the denominator.
Simplify the square root in denominator.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 4b
Simplify the quotient.
Multiply by a form of 1 to get a perfectsquare radicand in the denominator.
Simplify the square root in denominator.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Check It Out! Example 4c
Simplify the quotient.
Multiply by a form of 1 to get a perfectsquare radicand in the denominator.
Simplify the square root in denominator.
Factor and simplify the square root in
the numerator.
Holt Algebra 1
Multiplying and Dividing
11-8 Radical Expressions
Lesson Quiz
Multiply. Write each product in simplest form.
1.
2.
3.
4.
5.
6.
7.
Simplify each quotient.
8.
Holt Algebra 1
9.