Calculating the Nth root of a number manually is not an easy task. You can use Microsoft Excel to do these types of complicated calculations easily as well as accurately.
First, we will understand the meaning of roots.
What is the Nth Root of a Number?
Roots are the inverse operations of the exponents.
For example, 3 raised to the 2nd power is 9.
Therefore, the 2nd root (the 2nd root is often called the square root) of 9 is 3.
In this lesson, you will learn three different methods that you can use to find the Nth root of real numbers in Excel.
Method 1 – Calculate Nth Root in Excel Using the POWER Function
Below I have a data set where I have the numbers in column A and the indexes (Denoted by the letter N) in column B.
Now, I want to find the Nth root (as per the index) for each number in column C.
You can use the Excel POWER function to find the Nth root of any real number in Excel.
Below is the formula that you can enter in cell C2 to find the given root in cell B2 of cell A2.
=POWER(A2,1/B2)
The POWER function has 2 required arguments. The syntax of the POWER function is POWER (number, power).
You have to select the base number for the “number” argument. You can use any real number for that.
You can either select the cell that contains the base number or type the number manually. In this case, I have selected cell A2.
The base number’s exponent is indicated by the second argument, power. Since the index can be shown as a fractional exponent, we can enter the index as a fractional exponent.
Therefore, you have to type 1 divided by the index as the power.
For Calculating 2nd Root, Use SQRT Function
If you are finding the 2nd root of a number, you can also use the SQRT function. For example, our first calculation is to find the 2nd root of 4.
So, you can apply the SQRT function.
Then, you can use the below function.
=SQRT(A2)
The syntax of the SQRT function is SQRT(number).
The number is the only required argument for this function, and you can simply select the number from which you need to find the 2nd root (the square root) for this function.
If you need to find any Nth root other than the 2nd root, you have to use the POWER function.
Also read: How to Square a Number in Excel
Method 2 – Calculate Nth Root in Excel Using the Caret (^) Operator with Fractional Exponent
Another easy way to calculate the Nth root of a number is to use the caret operator.
Below I have a data set where I have the numbers in column A and the indexes (Denoted by the letter N) in column B.
Now, I want to find the Nth root (as per the index) for each number in column C.
Below is the formula that you can enter in cell C2 to find the given root in cell B2 of cell A2.
=A2^(1/B2)
First, you have to select the number from which you want to find the Nth root. Then enter the caret operator.
To insert the caret function, you have to hold the “CTRL” key and press “6”. Next, enter 1 divided by the index (N) within parentheses.
It is essential to enter the last expression within parentheses. Otherwise, the formula will find the 1st power of the number and divide it by the index. Then, your answers will be incorrect.
Also read: Euler’s Number in Excel (Using e in Excel)
Method 3 – Calculate Nth Root in Excel Using the Caret (^) Operator with Decimal exponent
When you are using the Nth root using the caret operator, you can insert the power as a decimal number.
Then, you don’t need to insert parentheses for the power.
Below I have a data set where I have the numbers in column A and the indexes (Denoted by the letter N) in column B.
Now, I want to find the Nth root (as per the index) for each number in column C.
You can follow the below steps to find the Nth root of a number using the caret operator with a decimal value.
Step 1 – First, create a new column as “Power” and find the reciprocal of N (Index) as a decimal value.
Below is the formula that you can enter in cell C2 to find the reciprocal of N (Index) of cell B2 as a decimal value.
=1/B2
Step 2 – Then, you have to use the below formula to find the Nth root.
Below is the formula that you can enter in cell D2 to find the given root in cell B2 of the number in cell A2.
=A2^C2
If you enter a negative number with an even index to find the Nth root, you will get a #NUM! Error. This happens because the function cannot calculate that.
You will get the Nth root for a negative number only if the index is an odd number.
In the below example, all the numbers are given as negatives. There is #NUM! Error for the numbers with even index.
In this lesson, you have learned how to find the Nth root in Excel using functions as well as formulas.
Using the POWER function is the easiest way to get the answer, as you don’t need to bother about inserting parentheses or new columns for converting indexes into decimal values.
Other Excel articles you may also like:
