SECTION 5.3 SIMPLIFIED FORM FOR RADICALS

RADICAL NOTATION:
For a real number x and a natural number n, if is a real number, , the principal nth root of x.

If no index is written, is interpreted as the square root of x, with index 2.

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Writing Expressions with Rational Exponents in Radical Form:

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For any real number x, if n is an even natural number if n is an odd natural number.  In particular,

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Assume all variables are non-negative values.

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Properties of Radicals

If are both real numbers, then

                            Radical Form                                     Exponential Form

, for

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Simplifying Radicals

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Simplified Form for Radical Expressions

A radical expression is in simplified form if and only if all of the following conditions are satisfied.

    The radicand is as small as possible; that is the exponent of m is less than the exponent of n.

    There are no fractions in the radicand.

There are no radicals in the denominator.

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Break down the radicand into something that you can take the root of and something that you can’t. Then simplify.