Roots of Real Numbers and Radical Expressions. Definition of n th Root. For any real numbers a and b and any positive integers n , if an = b , then a is the n th root of b . ** For a square root the value of n is 2. radical. index. radicand. Notation.
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For any real numbers a and b and any positive integers n,
if an = b,
then a is the nth root of b.
** For a square root the value of n is 2.
Note: An index of 2 is understood but not written in a square root sign.
Solution: = 3Simplify
To simplify means to find x in the equation:
x4 = 81
Opposite of principal square root
Both square rootsPrincipal Root
The nonnegative root of a number
no real roots
one + root one - root
one real root, 0
one + root no - roots
no + roots one - root
If the index (n) of the radical is even, the power under the radical sign is even, and the resulting power is odd, then we must use an absolute value sign.