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Fractional powers and real roots

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We have a special expression for symbolizing the real root of a number. We say that a^1/n represents the real root of a number if and only if n is even and a is positive. If these conditions obtain, then we have the principal nth root of the number a. This is precisely what is intended when we see a radicand under a square root symbol with an n to the upper left of the square root. This n represents the nth root of the radicand. For example, if we have 64 under a square root sign, and the number 5 where the n variable would normally be, to the upper left of the square root symbol, our answer is 4, since the 5th root of 64 is 4. The reader might be interested to know that the square root implies a 2 as the index. This is precisely why it's called the "square" root.



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