Square Root Calculator to
Find Square Root of a Number

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The online Square Root Calculator on this page is useful for quickly calculating square roots.

This free online square roots calculator will calculate the square root of a number and indicate whether or not the radicand is a perfect square.

Plus, unlike other sites with a radicand calculator, if the radicand is not a perfect square this calculator will calculate the nearest perfect squares that are greater and less than the entered radicand.

If you would like to find the square (or any other power) of a number, please visit the exponent calculator.

What are Square Roots?

Definition of a square root: The opposite of squaring a number. For example, finding the square root of 81 is the same as asking, "what number when squared is equal to 81?"

Of course, if you know that 9 x 9 = 81, you will know that the square root of 81 is 9 (92 = 81). However, what you might not realize is that -9 is also a square root of 81, because -9 x -9 also equals 81.

In other words, all numbers greater than zero (zero can never be negative or positive) have two square roots -- one positive and one negative. This is why when using an online square root calculator the result will always be preceded by a ± sign.

As for negative numbers, since a negative times a negative always yields a positive number, negative numbers cannot have a real value square root.

What Are Perfect Squares?

When a number has a square root that is a whole number, that number is said to be a perfect square. For example, since √4 has a square root of 2, 4 is said to be a perfect square. Here is a list of the perfect squares up to 225:

List of Perfect Squares up to 225

√1=1since12=1
√4=2since22=4
√9=3since32=9
√16=4since42=16
√25=5since52=25
√36=6since62=36
√49=7since72=49
√64=8since82=64
√81=9since92=81
√100=10since102=100
√121=11since112=121
√144=12since122=144
√169=13since132=169
√196=14since142=196
√225=15since152=225

With that, let's use the Square Root Calculator for finding the square root of a number.

Square Root Calculator
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Instructions: Enter the radicand and then click the "Calculate Square Root" button.

Note that you can enter non-negative decimal numbers for the radicand. This also means that if you wish to find the square root of a fraction, simply convert the fraction to a decimal and then enter the decimal.

Mouse over the blue question marks for a further explanation of each entry field. More in-depth explanations can be found in the glossary of terms located beneath the Square Root Calculator.

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Square Root Calculator Glossary of Terms

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Perfect squares: Numbers that are equal to a whole number squared (see the list of perfect squares above the square root calculator).

Radicand: The radicand is the number inside the radical sign (√), whereas the index is located to the left and above the radical sign. Enter the radicand (the number you are trying to find the square root of), which can be any number greater than or equal to zero.

Square roots: This is result of the square root calculation. If the result is a whole number the entered radicand is a perfect square. Otherwise, if the result is a short decimal, the entered decimal may have a real square root. However, if the result is a lengthy decimal number then the result is most likely an irrational number, which means the result is merely an approximation. In any case, results that are greater than zero will always represent two square roots (one positive and one negative).

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