 Online Calculators

# Square Root Calculator

Square Roots Calculator
$$\sqrt[]{x} = \; ?$$

## Calculator Use

Use this calculator to find the principal square root and roots of real numbers. Inputs for the radicand x can be positive or negative real numbers. The answer will also tell you if you entered a perfect square.

## Square Roots, odd and even:

There are 2 possible roots for any positive real number. A positive root and a negative root. Given a number x, the square root of x is a number a such that a2 = x. Square roots is a specialized form of our common roots calculator.

"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.".

## Perfect Square Calculator

This calculator will also tell you if the number you entered is a perfect square or is not a perfect square.  A perfect square is a number x where the square root of x is a number a such that a2 = x and a is an integer. For example, 4, 9 and 16 are perfect squares since their square roots, 2, 3 and 4, respectively, are integers.

## Example Square Roots:

• The 2nd root of 81, or 81 radical 2, or the square root of 81 is written as $$\sqrt{81} = \sqrt[]{81} = \pm 9$$.
• The 2nd root of 25, or 25 radical 2, or the square root of 25 is written as $$\sqrt{25} = \sqrt[]{25} = \pm 5$$.
• The 2nd root of 100, or 100 radical 2, or the square root of 100 is written as $$\sqrt{100} = \sqrt[]{100} = \pm 10$$.
• The 2nd root of 10, or 10 radical 2, or the square root of 10 is written as $$\sqrt{10} = \sqrt[]{10} = \pm 3.162278$$.

To calculate fractional exponents use our calculator for Fractional Exponents.

### References

 Weisstein, Eric W. "Square Root." From MathWorld -- A Wolfram Web Resource. Square Root