Square Root Calculator
Find the square root of any number. Handles negative numbers with imaginary results.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the Square Root Calculator
Enter any number and the square root appears instantly. No buttons needed. The result updates as you type.
- Enter a number. Type any positive or negative number, including decimals.
- Read the result. For positive numbers, you get the principal (positive) square root. For negative numbers, the calculator returns the imaginary result.
- Copy or share. Use the buttons below the result to copy the value or share a link.
About Square Roots
The square root of a number x is the value that, when multiplied by itself, gives x. For example, the square root of 144 is 12, because 12 x 12 = 144. Perfect squares like 4, 9, 16, 25, and 36 have whole-number square roots. Most numbers have irrational square roots that go on forever without repeating.
Negative numbers have imaginary square roots. The square root of -1 is defined as "i" (the imaginary unit). So the square root of -4 is 2i. This calculator handles both real and imaginary results automatically.
Frequently Asked Questions
What is the square root of a negative number?
The square root of a negative number is an imaginary number. For example, sqrt(-9) = 3i, where "i" represents the imaginary unit (the square root of -1).
What is a perfect square?
A perfect square is a number whose square root is a whole number. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. The number 144 is also a perfect square because sqrt(144) = 12.
How do I simplify a square root?
To simplify a square root, factor the number into a perfect square and another factor. For example, sqrt(72) = sqrt(36 x 2) = 6 x sqrt(2). This calculator gives the decimal result directly.