Root Calculator
Find the nth root of a number, including odd roots of negatives, with the result shown as a power check.
Example
The cube root of 27 (value = 27, n = 3):
27^(1/3) = 3 because 3 × 3 × 3 = 27
The 5th root of -32 (value = -32, n = 5) gives -2, since (-2)^5 = -32. But the square root of -32 (n = 2, even) has no real result.
How it works
Enter the value and the root degree n, then read the nth root instantly. For negative values, the calculator returns a real root only when n is odd.
Good to know
The Root Calculator finds the nth root of any number you enter — the square root by default, but also cube roots, 4th roots, or any custom degree you choose. You type a value (x) and a root degree (n), and it returns the real number that, raised to the power n, gives you back x. It's built for students working through radicals and exponents, anyone reversing a power in algebra or geometry, and people who just need a quick, no-frills root without opening a spreadsheet.
Reach for it whenever you have the result of a repeated multiplication and want the base back: finding a side length from a volume (cube root), recovering a growth rate from a multi-period factor, or simplifying expressions where a radical sits under the n. Setting n to 2 gives the familiar square root; n to 3 gives the cube root; larger or fractional-looking cases just change the degree field.
The result is shown in three supporting ways so you can trust it. The big number is the nth root itself; the "Check (root^n)" stat raises that answer back to the power n so you can confirm it lands on your original value; and "As exponent" restates the operation as x raised to 1/n, which is the same thing written in power form. If you see "no real root," the calculator is telling you that an even root of a negative number has no real value.
One practical caveat: results are rounded for display (to about ten significant figures), so a root that should be a clean integer may occasionally show a tiny rounding artifact, and the check value won't always be perfectly exact for irrational roots. Negative inputs only return a real answer when n is odd — for even degrees of negatives, you'd need complex numbers, which this tool intentionally doesn't cover.
Frequently asked questions
Why does a negative value sometimes show "no real root"?
Even roots (like the square or 4th root) of a negative number have no real value, because no real number raised to an even power is negative. The calculator only returns a real root of a negative value when the degree n is odd (e.g. the cube root of -8 is -2).
How do I compute a square root with this tool?
Leave the root degree n set to 2 (the default math case). The value's square root is then shown, for example value 16 with n = 2 returns 4.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
What is the nth root of a number?
The nth root of x is the number that, when multiplied by itself n times, equals x. For example, the 4th root of 81 is 3 because 3 × 3 × 3 × 3 = 81. It is the inverse of raising a number to the nth power.
How do you write a root as an exponent?
The nth root of x is the same as x raised to the power 1/n. So the cube root of x equals x^(1/3), and the square root equals x^(1/2). This is why the tool shows an 'As exponent' form alongside the answer.
Can you take the root of a fraction or decimal?
Yes. The root of a fraction or decimal follows the same rule as whole numbers; for instance the square root of 0.25 is 0.5. Just enter the decimal value and the desired degree.
What is the difference between a square root and a cube root?
A square root (degree 2) finds a number that multiplies by itself twice to reach the value, while a cube root (degree 3) finds one that multiplies by itself three times. Square roots of negatives have no real value, but cube roots of negatives do.
Why does the cube root of a negative number have a real answer but the square root does not?
Cube root uses an odd degree, and a negative number raised to an odd power stays negative, so a real negative root exists. Square root uses an even degree, and no real number squared can be negative, so there is no real square root of a negative.
Is the nth root the same as dividing by n?
No. Dividing by n splits a number into n equal parts, while the nth root finds a base that, multiplied by itself n times, reproduces the number. For example 1/3 of 27 is 9, but the cube root of 27 is 3.
How can I check if a root result is correct?
Raise the result back to the power n and see if you get the original value. The calculator does this automatically in its 'Check (root^n)' field, though irrational results may differ slightly due to rounding.
Does every number have just one real nth root?
For odd degrees, each real number has exactly one real nth root. For even degrees, positive numbers technically have two real roots (a positive and a negative), and this tool reports the principal, non-negative one.
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