Raises a number to a power, or finds its square, cube or nth root. Switch between the two with the buttons.
Key terms
- Base — the number being multiplied.
- Exponent — how many times, or a fraction for a root.
- Degree — which root: 2 is square, 3 is cube.
How it works
Power and root
power = baseexponent · root = base1/n
A root is a fractional power: the square root of 16 is 16 to the power one half.
What has no real answer
The square root of a negative number is not a real number — nothing multiplied by itself gives a negative result. The cube root of a negative number is real and negative, because an odd number of negative factors stays negative: the cube root of −27 is −3. A negative base raised to a fractional power, like −2 to the power 0.5, has no real result either, for the same reason as the square root case. This calculator declines rather than showing an error or a wrong number.
How to use this calculator
- Choose power or root.
- Enter the numbers.
- Read the result. If nothing appears, the answer is not a real number.
Frequently asked questions
Why does the square root of a negative number give nothing?
No real number multiplied by itself produces a negative result, since a negative times a negative is positive. The result exists only in complex numbers, which this calculator does not cover.
Why is the cube root of a negative number different?
Multiplying three negative numbers gives a negative result, so a negative number does have a real cube root, and it is negative.
What is a number to the power zero?
1, for any nonzero base. 0 to the power 0 is taken as 1 here by convention rather than derived from repeated multiplication.
What does a negative exponent mean?
One over the positive power: 2 to the power −2 is 1 divided by 2 squared, which is 0.25.
Is there a limit to which root I can take?
Not mathematically, though this calculator caps the degree at 20 — beyond that the answer converges so close to 1 that the extra precision has no practical use.
