Square Root Calculator
Any root, with the simplified surd where one exists.
Work out Square Root. Any root, with the simplified surd where one exists. Shows the working, not just the answer.
2 for square root, 3 for cube root.
Square root
8.48528137
Exact form: 6√2
72 is not a perfect square, but it factors into one: 6√2. Pulling out the largest square factor gives an exact form, which is preferred in algebra because 8.485281 is a rounded decimal while 6√2 is precisely right.
How the Square Root Calculator works
Square roots, cube roots and any nth root, with the exact simplified form alongside the decimal. √72 is 8.485 as a decimal but exactly 6√2 in surd form, and the second is what algebra wants. Odd roots of negative numbers work too, which the naive power function gets wrong.
Also known as: cube root calculator · nth root calculator · simplify a square root · radical calculator
Frequently asked questions
How do I simplify a square root?
Pull out the largest perfect square factor. 72 is 36 × 2, so √72 becomes 6√2 — exact, where the decimal 8.485 is only a rounding.
What is the cube root of a negative number?
A negative number. The real cube root of −8 is −2. Most power functions return an error here because they decline to choose among three complex roots, so this handles the sign separately.
Why can't I take the square root of a negative?
Because nothing real, squared, gives a negative. Even roots of negatives exist only in complex numbers; odd roots are fine.
What makes a number irrational?
Its decimal never terminates or repeats. √2 is the classic example — no fraction equals it exactly, so any decimal shown is a rounding.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
<iframe src="https://www.thecalclibrary.com/embed/square-root-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Square Root Calculator"></iframe>The only condition is that the credit line stays visible. It sits inside the frame, so you do not have to do anything to keep it.
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