Nth Root Calculator Excel

An nth root calculator helps you find the root of a number when you know the index. This guide explains how to calculate roots in Excel, understand the formula, and apply it to real-world problems.

What is an nth root?

The nth root of a number is a value that, when raised to the power of n, gives the original number. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27.

Common roots include:

Square root (2nd root)
Cube root (3rd root)
Fourth root (4th root)
Fifth root (5th root)

In Excel, you can calculate roots using the POWER function combined with the inverse operation.

How to calculate nth root

To find the nth root of a number:

Identify the radicand (the number under the root) and the index (n)
Use the formula: root = radicand^(1/n)
For example, the 4th root of 16 is 16^(1/4) = 2

Formula: root = radicand^(1/n)

This formula works for any positive real number and any positive integer n.

Excel formula for nth root

In Excel, you can calculate nth roots using the POWER function:

=POWER(radicand, 1/n)

For example, to find the cube root of 27 in cell B2:

=POWER(27, 1/3)

This will return 3.0, which is the cube root of 27.

Note: Excel's POWER function can handle both positive and negative radicands, but the result may be complex for negative radicands with even roots.

Examples of nth roots

Here are some examples of nth roots calculated in Excel:

Radicand	Index (n)	Root	Excel Formula
16	2	4	=POWER(16, 1/2)
8	3	2	=POWER(8, 1/3)
16	4	2	=POWER(16, 1/4)
32	5	2	=POWER(32, 1/5)

These examples show how to calculate different roots in Excel using the POWER function.

FAQ

What is the difference between a square root and a cube root?: The square root is the 2nd root, while the cube root is the 3rd root. The square root of a number is a value that, when multiplied by itself, gives the original number. The cube root is a value that, when multiplied by itself three times, gives the original number.
Can I calculate roots of negative numbers in Excel?: Yes, you can calculate roots of negative numbers in Excel, but the result may be complex. For example, the square root of -1 is i (the imaginary unit), which Excel represents as a complex number.
What happens if I try to calculate a root with a non-integer index?: Excel's POWER function can handle non-integer indices, but the result may not be as straightforward as with integer indices. For example, the 1.5th root of 8 is 4, but the 1.5th root of 9 is approximately 2.478.
Is there a simpler way to calculate roots in Excel than using the POWER function?: Yes, you can use the caret (^) operator in Excel, which is equivalent to the POWER function. For example, =16^(1/2) is the same as =POWER(16, 1/2).
Can I calculate roots of fractions in Excel?: Yes, you can calculate roots of fractions in Excel. For example, the cube root of 1/8 is 1/2, which you can calculate using =POWER(1/8, 1/3).