Algebra and General Mathematics: Radicals

RADICALS

A radical is an expression of the form ⁿ√x which denotes the principal n^th root of x.

ⁿ√x = x^(1/n)

where:

n – index

x – radicand

√ – radical sign or symbol

in terms of fractional exponent:

ⁿ√x^m = (ⁿ√x)^m = x^m/n

PROPERTIES OF RADICALS

1. ⁿ√x^m = (ⁿ√x)^m

      2. ⁿ√x ·ⁿ√y = ⁿ√(xy)

                       3. (ⁿ√x) / (ⁿ√y) = ⁿ√(x/y), y ≠ 0

  4. ^m√(ⁿ√x) = ^mn√x

5. (ⁿ√x)ⁿ = x

                6. (ⁿ√xⁿ) = | x |, (n = even)

              (ⁿ√xⁿ) = x, (n = odd)

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