Please Note: This article is written for users of the following Microsoft Excel versions: 2007, 2010, 2013, and 2016. If you are using an earlier version (Excel 2003 or earlier), this tip may not work for you. For a version of this tip written specifically for earlier versions of Excel, click here: Finding the Nth Root of a Number.

Finding the Nth Root of a Number

by Allen Wyatt
(last updated November 9, 2020)

6

You may be wondering how to use Excel to derive different roots of a number. Finding a square root is easy: you just use the SQRT function. For instance, the following returns the square root of the value in cell B7:

=SQRT(B7)

What about different roots, however? What if you want the fifth root of the value in B7, instead of the square root? Unless you are a math whiz (and I am not), the answer may not be that obvious. All you need to do is raise the value to the power of 1/n. For instance, if you want that fifth root of B7, then you would use the following formula:

=B7^(1/5)

ExcelTips is your source for cost-effective Microsoft Excel training. This tip (12350) applies to Microsoft Excel 2007, 2010, 2013, and 2016. You can find a version of this tip for the older menu interface of Excel here: Finding the Nth Root of a Number.

Author Bio

Allen Wyatt

With more than 50 non-fiction books and numerous magazine articles to his credit, Allen Wyatt is an internationally recognized author. He is president of Sharon Parq Associates, a computer and publishing services company. ...

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What is five more than 8?

2020-11-13 06:46:18

Peter Atherton

Ronald Finnerty
A couple of useful links'

https://www.exploringbinary.com/binary-converter/
https://indepth.dev/the-simple-math-behind-decimal-binary-conversion-algorithms

Unfortunately, neither how to get the square root of a binary number. Here are the basics:

(see Figure 1 below)

You can convert a whole number to binary using the DEC2BIN function or by an algorithm shown in Fig1. It also shows how to convert a decimal to binary. Some decimals can not be converted exactly, so we stop when you get a repeated pattern.

For the decimal algorithm, you can use the TEXTJOIN function to get the decimal part from the algorithm.

To get a square root you can use the Babylonian algorithm {fig2), I just used the SQRT function in K2 of 65 to get the integer binary. And used a version of the TEXTJOIN for the decimal part.

(see Figure 2 below)

Of course, you don't need the Babylonian algorithm for the fraction just get it from the decimal SQRT function.

Figure 1. Integer & Faction convertsion.

Figure 2. Babylonian Fraction Algorithm


2020-11-12 05:47:03

JMJ

I'm afraid there is serious confusion here:

- n^(1/5) gives the fifth root of n
- n^-(5 ) gives the inverse of n^5

By example, if n = 10,
n^2 = 100
n^-2 = 0.01
n^(1/2) = 3.16227766 (this is the square root of 10)

So, using fractional exponents or negatives exponents is COMPLETELY DIFFERENT !


2017-09-25 10:20:04

Ronald Finnerty

this did not answer the finding nth root question. It merely shows how nth root calculation work.
If I have a number and need to find the nth root of base 2 of the number i am no further along with your solution.
i only know the answer is 2^1/n so how do i find n?


2017-06-20 09:22:53

Dennis Costello

Just to be pedantic, I'll point out that Maarten is almost correct. He said:
2^-1 for instance is 0.5 (2/2^1)
2^-3 is 0.125 (2/2^3)
When he meant
2^-1 for instance is 0.5 (1 / 2^1)
2^-3 is 0.125 (1 / 2^3)


2016-06-30 17:20:39

Maarten Daams

You can even use negative exponents.
2^-1 for instance is 0.5 (2/2^1)
2^-3 is 0.125 (2/2^3)
etc.
And so on.
Of course fractional negative exponents work also, but that is more complicated


2016-06-11 06:08:43

Polarisking

The POWER function also works here,

POWER(B7,1/5)


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