Raise a Number to a Fraction to Find the Square or Third Root

March 07, 2022 - by Bill Jelen

Problem: Excel offers a SQRT function to find the square root of a number. What do I do if I need to figure out the third root or the fourth root of a number?

Strategy: You can raise a number to a fraction to find a root. To find the square root of a number, you can raise the number to the 1/2 power. To find the cube root of a number, you can raise the number to the 1/3 power. To find the eighth root of a number, you can raise the number to the 1/8 power.

Let’s look at several examples.

If you need to find the square root, you can use the SQRT function.

D2 contains 64. Calculate the square root using =SQRT(D2). This gives you eight, because 8*8 is 64. — Figure 358. SQRT is a built-in function for square roots.

To calculate a square root, you can raise a number to the one-half (1/2) power. Since (1/2) is a rational number, you could alternatively use =D2^0.5.

Another way to calculate a square root is to raise the number to the 1/2 power. =D2^(1/2). There really is a point to this, as you will see in the next image. — Figure 359. Raising to a fraction takes the root.

To find the cube root of a number, you can raise the number to the one-third (1/3) power.

Excel has functions for square root, but not cube roots. What number when multiplied by itself three times is 125? Put 125 in D2 and use =D2^(1/3) to calculate the cube root of 5. — Figure 360. For cube roots, raise to the 1/3 power.

To find the fourth root of a number, you raise the number to either the one-fourth (1/4) or 0.25 power.

The fourth root of 16 is 2. Put 16 in D2 and then calculate =D2^(1/4) — Figure 361. Raise to the 1/4 power.

You can find any root in the same way: To find the nth root, you simply raise the number to the 1/n power. For example, to find the 17th root of a number, you raise it to the one-seventeenth (1/17) power.

To figure out the 17th root of a number, use =D2^(1/17) — Figure 362. Find the nth root by raising to 1/n.

Although Excel only offers a function for a square root, you can use the technique of raising to a fractional power in order to determine any root of a number.

This article is an excerpt from Power Excel With MrExcel

Title photo by Eilis Garvey on Unsplash