Information

Even Index Roots


When we raise a positive number or a negative number to an even exponent, the result is always a positive number.

Example:

(-4)² = (-4)(-4) = 16
and
(+4)² = (+4)(+4) = 16

However, as in mathematics the result of an operation must be unique, it is defined that:

Generically:

Any even index root of a positive number is the positive number that raised to the exponent corresponding to that index equals the given number.

Note:

There is no real root of a negative number if the index is even.

Example:

doesn't exist because there is no real number that squared gives - 4.

Next: Odd Index Roots