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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Roots of Real Numbers and Radical Expressions
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: = 3
To simplify means to find x in the equation:
x4 = 81
Principal square root
Opposite of principal square root
Both square roots
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.