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

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

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.

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Figure 364 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.

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Figure 365 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.

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Figure 366 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.

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Figure 367 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.

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Figure 368 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.

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