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Published byJonathan Singleton Modified over 4 years ago

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Simplifying

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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???

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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

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Let’s do a few problems together. Factor into squares Product Property of Radicals

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Factor into cubes if possible Product Property of Radicals

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Now, you try these examples.

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Quotient Property of Radicals 0,For real numbers a and b, b And any integer n, n>1, Ex:

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In general, a radical expression is simplified when: 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.

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Simplify each expression. Rationalize the denominator Answer

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To simplify a radical by adding or subtracting you must have like terms. Like terms are when the powers AND radicand are the same.

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Here is an example that we will do together. Rewrite using factors Combine like terms

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Try this one on your own.

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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.

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Since there are no like terms, you can not combine.

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Lets do another one.

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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.

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Simplify: Multiply by the conjugate. FOIL numerator and denominator. Next

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Combine like terms Try this on your own:

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Here are a mixed set of problems to do.

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