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Square Root Calculator.
Find the square root of any number as a decimal and in simplified radical form, such as √72 = 6√2.
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How to Use
The square root of a number is the value that multiplies by itself to give that number. 12 x 12 = 144, so the square root of 144 is 12.
Simplified radical form pulls the largest perfect-square factor out from under the radical sign: √72 = √(36 x 2) = 6√2. It is the exact answer, unlike a rounded decimal.
Negative numbers have no real square root, so this calculator asks for a number of 0 or more. Decimals are supported but are only shown as a decimal answer, not as a radical.
FAQs
How do you simplify a square root?
Find the largest perfect square that divides the number, then take its root outside the radical. For √72, the largest perfect-square factor is 36, so √72 = √(36 x 2) = 6√2. Simplified radical form is exact, unlike a rounded decimal such as 8.485.
What is a perfect square?
A perfect square is a number whose square root is a whole number, because it is some integer multiplied by itself: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 and so on. When you enter one, this calculator flags it and the radical disappears entirely — √144 is simply 12.
Why is √72 equal to 6√2?
72 factors as 36 x 2, and 36 is a perfect square. Since √(a x b) = √a x √b, you get √36 x √2 = 6√2. Stopping at 4 x 18 would give 2√18, which is correct but not fully simplified — always pull out the largest perfect square.
Can you take the square root of a negative number?
Not within the real numbers: any real number multiplied by itself is zero or positive, so nothing squares to a negative. Mathematicians define imaginary numbers for this (√-9 = 3i), but this calculator works in real numbers and asks for an input of 0 or more.
What is the square root of 0 and of 1?
Both are perfect squares and are their own square roots: √0 = 0 because 0 x 0 = 0, and √1 = 1 because 1 x 1 = 1. They are the only two numbers that equal their own square root.
Can I enter decimals?
Yes. The decimal square root is calculated for any non-negative number, so √2.25 = 1.5. Radical simplification is only shown for whole numbers, because pulling perfect-square factors out of a decimal has no standard simplified form.