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## 6.2 Products and Quotients of Radicals

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**6.2 Products and Quotients of Radicals**Algebra II Mrs. Spitz Spring 2007**Objectives:**• Simplify radical expressions using multiplication and division, and • Rationalize the denominator of a fraction containing a radical expression.**Assignment**• pg. 262 #5-52**2 Methods**• Method 1:**2 Methods**• Method 2: The result is the same using either method. These examples demonstrate the following principle on the next slide.**Product Property of Radicals**• For any real numbers a and b, and any integer n, n > 1, • If n is even, then as long as a and b are both nonnegative, and • if n is odd, then When you simplify a square root, first write the prime factorization of the radicand. Then use the product property to isolate the perfect squares. Then simplify each radical.**Ex. 1: Simplify**If a < 0, then has no real roots, so we must assume that a ≥ 0, we don’t need to write However, b could be negative so we write as |b|.**Take a look at the division of radicals to see if there is a**quotient property similar to the product property of radicals. What do you think we’ll discover?**Take a look at the division of radicals to see if there is a**quotient property similar to the product property of radicals. What do you think we’ll discover?**Quotient Property of Radicals**For any real numbers, a and b, b ≠ 0, and any integer n, n > 1, if all roots are defined.**A radical expression is simplified when the following**conditions are met: • The index, n, is as small as possible. • The radicand contains no factor (other than one) which is the nth power of an integer or polynomial. • The radicand contains no fractions. • No radicals appear in the denominator.**Reminder:**• Friday, Jan. 19th is MAPS testing for 2nd and 6th periods. You must be here, or it will take you longer to make it up. Since I am giving you a grade (activity) for MAPS testing; I expect you to be there. Deficiencies come up very soon this quarter, and not testing will drop your grade 10%.