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Square Root Calculator
Square Root Calculator
Use this calculator to find the square root of positive numbers; it accepts inputs of positive real numbers for the radicand. There are 2 possible roots for a square root; the positive root and the negative root. Given a number n, the square root of n is a number a such that a2 = n. Square roots is a specialized form of our common roots calculator also know as a radicals calculator. The answer will also indicate if you entered a perfect square.
Square Roots:
"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].
Perfect Square Calculator
This calculator will also tell you if the number you entered is a perfect square. A perfect square is a number n where the square root of n is a number a such that a2 = n 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 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