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## Simplifying

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**Simplifying**Radical Expressions**When simplifying a radical expression, find the factors that**are to the nth powers of the radicand and then use the Product Property of Radicals. What is the Product Property of Radicals???**For any real numbers a and b, and any integer n, n>1,**1. If n is even, then When a and b are both nonnegative. 2. If n is odd, then Product Property of Radicals**Let’s do a few problems together.**Factor into squares Product Property of Radicals**Product Property of Radicals**Factor into cubes if possible Product Property of Radicals**For real numbers a and b, b**0, And any integer n, n>1, Quotient Property of Radicals Ex:**The radicand contains no fractions.**No radicals appear in the denominator.(Rationalization) The radicand contains no factors that are nth powers of an integer or polynomial. In general, a radical expression is simplified when:**Simplify each expression.**Rationalize the denominator Answer**To simplify a radical by adding or subtracting you must have**like terms. Like terms are when the powers AND radicand are the same.**Here is an example that we will do together.**Rewrite using factors Combine like terms**You can add or subtract radicals like monomials. You can**also simplify radicals by using the FOIL method of multiplying binomials. Let us try one.**When there is a binomial with a radical in the denominator**of a fraction, you find the conjugate and multiply. This gives a rational denominator.**Simplify:**Multiply by the conjugate. FOIL numerator and denominator. Next**Combine like terms**Try this on your own: