Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.
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Transcript of Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.
![Page 1: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/1.jpg)
Including Rationalizing The Denominators
![Page 2: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/2.jpg)
Warm Up
Simplify each expression.
1.
2.
3.
4.
![Page 3: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/3.jpg)
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.
![Page 4: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/4.jpg)
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
![Page 5: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/5.jpg)
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
![Page 6: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/6.jpg)
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
![Page 7: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/7.jpg)
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.
![Page 8: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/8.jpg)
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.
![Page 9: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/9.jpg)
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.
![Page 10: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/10.jpg)
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
![Page 11: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/11.jpg)
Using the Distributive Property
Multiply. Write the product in simplest form.
Product Property of Square Roots.
Distribute
Simplify the radicands.
Simplify.
![Page 12: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/12.jpg)
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
![Page 13: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/13.jpg)
Try This!
Multiply. Write the product in simplest form.
Product Property of Square Roots.
Simplify the radicand.
Simplify.
Distribute
COPY
![Page 14: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/14.jpg)
Try This!
Multiply. Write the product in simplest form.
Product Property of Square Roots.
Simplify the radicand.
Simplify.
Distribute
![Page 15: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/15.jpg)
Try This!
Multiply. Write each product in simplest form.
Product Property of Square Roots.
Simplify the radicand.
Simplify.
Distribute
![Page 16: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/16.jpg)
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.
![Page 17: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/17.jpg)
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
![Page 18: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/18.jpg)
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
![Page 19: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/19.jpg)
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.
![Page 20: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/20.jpg)
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
![Page 21: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/21.jpg)
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
![Page 22: Including Rationalizing The Denominators. Warm Up Simplify each expression. 1. 2. 3. 4.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f125503460f94c26364/html5/thumbnails/22.jpg)
Lesson Quiz
Multiply. Write each product in simplest form.
1.
3.
Simplify each quotient.
5.
7. 8.
2.
4.
6.