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Square Root Calculator

Calculate the square root of any number instantly, including both positive and negative inputs. For positive numbers, the calculator returns the principal (non-negative) real root. For negative numbers, it returns the complex result using imaginary number notation (i). The calculator also provides the squared verification so you can confirm the answer.

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Formula

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Core Formula
n\sqrt{n}

How it works: For n >= 0, the square root is the non-negative number that, when multiplied by itself, equals n. For example, sqrt(49) = 7 because 7 x 7 = 49. For n < 0, the result is expressed as i x sqrt(|n|), where i is the imaginary unit representing sqrt(-1).

Worked Example

sqrt(49) = 7, because 7 x 7 = 49.
sqrt(2) = 1.41421356..., an irrational number that continues infinitely without repeating.
sqrt(0.25) = 0.5, because 0.5 x 0.5 = 0.25.
sqrt(-49) = 7i, because (7i) x (7i) = 49 x i^2 = 49 x (-1) = -49.

Frequently Asked Questions

Can this calculate square roots of negative numbers?

Yes. Negative inputs produce complex (imaginary) results. For example, sqrt(-49) = 7i, where i is the imaginary unit. This is useful in electrical engineering, physics, and advanced mathematics.

How do I verify the result?

Square the result and confirm it equals your original number. For example, if sqrt(49) = 7, then 7 x 7 = 49 confirms the answer. The calculator shows this verification automatically.

What is the square root of 0?

The square root of 0 is 0, because 0 x 0 = 0. Zero is the only number that is its own square root alongside 1.

Are all square roots irrational?

No. Perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100...) have whole number square roots. Non-perfect squares like 2, 3, 5, 7 have irrational square roots that continue infinitely without repeating.

What is the difference between sqrt and cube root?

Square root finds a number that multiplied by itself gives the original. Cube root finds a number that multiplied by itself three times gives the original. For example, sqrt(9) = 3 but cbrt(27) = 3.

How can I put this Square Root Calculator on my blog or website?

Yes, the Square Root Calculator is fully embeddable. Tap "Embed" above to configure appearance and copy the code. It is free to use, works on any platform (HTML, WordPress, CMS), and adjusts to any screen size automatically. Visit calculory.com/services/embed-calculators for the complete guide.

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