Finding Square Roots, Cube Roots, and nth Roots in Excel

Excel's powerful mathematical toolkit includes functions for square roots, cube roots, and even nth roots.

Our review of these techniques will focus on the manual entry of formulas, but check out our tutorial on using Excel if you need a refresher on formula entry for core functions. A function's syntax refers to the layout of the function and includes the function's name, brackets, comma separators, and arguments.

How to Find Roots in Excel

1. Calculate a square root. The syntax for the SQRT() function is:

   =SQRT(number)
   

   For this function, you must only supply the number argument, which is the number for which a square root must be found. It can be any positive number or a cell reference to the location of the data in a worksheet.

   If a negative value is entered for the number argument, SQRT() returns the #NUM! error value––because multiplying two positive or two negative numbers together always returns a positive result, it is not possible to find the square root of a negative number in the set of real numbers.

2. Calculate an nth root. Use the POWER() function to calculate any root value:

   =POWER(number,(1/n))
   

   For the POWER() function, you'll supply as arguments both the number and its exponent. To calculate a root, simply supply an inverse exponent — for example, a square root is 1/2.

   The POWER() function is useful for both powers and exponents. For example:

   =POWER(4,2)
   

   yields 16, whereas:

   =POWER(256,(1/2))
   

   also yields 16, which is the square root of 256. Roots are the inverse of powers.

3. Find the cube root in Excel. To calculate the cube root of a number in Excel, use the caret operator (^) with 1/3 as the exponent in a simple formula.

   =number^(1/3)
   
   
   

   In this example, the formula =D3^(1/3) is used to find the cube root of 216, which is 6.

4. Calculate the roots of imaginary numbers. Excel offers the IMSQRT() and IMPOWER() functions to return roots and powers of imaginary numbers. The syntax of these functions is identical to the real-number versions.