Square Root Calculator

Instantly convert between a number x and its principal square root √x.

Step-by-step derivation

Enter any one field to see the derivation.

References

  • Square root (principal root) and definition (y^2=x).
  • Exponent notation (x^{1/2}) for (sqrt{x}).

Use this Square Root Calculator to find the principal square root of a nonnegative number or reverse the calculation by finding the original number from its square root.

Calculation Method

Square root:

y = √x

Reverse calculation:

x = y²

The radical symbol √ represents the principal, nonnegative square root.

Example

Find the square root of 144:

√144 = 12

because:

12 × 12 = 144

Important Note

This calculator works with real-number square roots. Negative numbers do not have real square roots and require complex-number mathematics.

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