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Square Root & Nth Root Calculator

Calculate the square root or any other root (nth root) of a number.

Nth Root Calculator

Calculate any root of a number.

Understanding Roots

Finding the root of a number is the inverse operation of raising a number to a power. The 'n'-th root of a number 'x' is a number 'y' such that yⁿ = x.

Common Roots

  • Square Root (n=2): The number that, when multiplied by itself, gives the original number. The square root of 9 is 3 because 3² = 9.
  • Cube Root (n=3): The number that, when multiplied by itself twice, gives the original number. The cube root of 8 is 2 because 2³ = 8.

Calculation Method

Calculating the n-th root is equivalent to raising the number to the power of 1/n.

ⁿ√x = x^(1/n)

This calculator uses this mathematical identity to find the root for any given number and root index 'n'.

What Is a Square Root and How Is It Calculated?

Finding the "root" of a number is the opposite of raising a number to a power. For example, we know that 3² = 9. The square root of 9 asks the question, "What number, when multiplied by itself, equals 9?" The answer is 3.

While the square root is the most common, you can find any "nth" root. I designed this calculator to solve for any root you need, whether it's a square root, a cube root, or the 5th root.

How to Use the Nth Root Calculator

Simply enter two values:

  • The Root (n): For a square root, enter 2. For a cube root, enter 3, and so on.
  • The Number (x): The number you want to find the root of.

How to Use This Nth Root Calculator

Calculating the nth root of a number 'x' is the same as raising 'x' to the power of 1/n.

ⁿ√x = x^(1/n)

This is the formula my calculator uses. For example, to find the cube root of 27 (³√27), it calculates 27^(1/3), which equals 3.

A Note on Negative Numbers

You can take an odd root (like a cube root) of a negative number. For example, the cube root of -8 is -2, because (-2) × (-2) × (-2) = -8.

However, you cannot take an even root (like a square root) of a negative number in the real number system. Doing so results in a "complex" or "imaginary" number, which this calculator does not support.

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