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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:.
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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%.