Square Roots Calculator

About this Calculator

This online calculator will calculate the principle square root of an entered number.

Notes on taking square roots:

Any number has 2 square roots, one positive and one negative. See notes below.

"Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3, since (-3)² = (+3)² = 9. Any nonnegative real number x has a unique nonnegative square root r; this is called the principal square root .......... For example, the principal square root of 9 is sqrt(9) = +3, while the other square root of 9 is -sqrt(9) = -3. In common usage, unless otherwise specified, "the" square root is generally taken to mean the principal square root."[1].

This calculator will find the square root of a number. It accepts inputs of positive real numbers for the radicand. Square roots is a specialized form of our common roots calculator also know as a radicals calculator. There are 2 possible roots for square roots. The positive root and the negative root.

Examples:

• The 2nd root of 81, or 81 radical 2, or the square root of 81 is written as 2√81 or √81= ±9
• The 2nd root of 25, or 25 radical 2, or the square root of 25 is written as 2√25 or √25= ±5
• The 2nd root of 100, or 100 radical 2, or the square root of 100 is written as 2√100 or √100= ±10
• The 2nd root of 10, or 10 radical 2, or the square root of 10 is written as 2√10 or √10 = ±3.162278

To calculate fractional exponents use our Fractional Exponents Calculator.

References

[1] Weisstein, Eric W. "Square Root." From MathWorld -- A Wolfram Web Resource. http://mathworld.wolfram.com/SquareRoot.html