CalcArcade.

Square Root Calculator

Enter a number and the root you want. 2 gives a square root, 3 a cube root and so on. For whole numbers you also get the exact simplified form and whether it is a perfect power.

Your numbers

Result

How we calculate it

The n-th root of a is a^(1/n). The calculator shows it to 10 significant digits, and shows a whole result exactly when there is one.

For a whole number, the exact form writes a = k^n × m with m as small as possible, using the prime factors. For example 72 = 6^2 × 2, so the square root of 72 is 6√2, which is about 8.485281374. If m is 1, the number is a perfect power and the root is the whole number k.

Assumptions and limits

  • An even root, such as a square root, of a negative number is not a real number. Odd roots of negative numbers are fine: the cube root of −27 is −3.
  • The simplified form is shown for whole numbers up to 1,000,000,000,000.
  • The root must be a whole number from 2 to 100.

Frequently asked questions

How do I simplify a square root?

Find the largest square that divides the number, take its root outside the radical, and leave the rest inside. 72 is 36 × 2, so the square root of 72 is 6√2.

What is a perfect square?

A perfect square is a whole number whose square root is also a whole number, such as 1, 4, 9, 16 and 144. The Perfect power? line tells you.

Can I take the square root of a negative number?

Not in the real numbers. The result would be an imaginary number, which this calculator does not handle. It does handle odd roots of negative numbers, such as a cube root.

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Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: Number = 72; Root (2 for square root, 3 for cube root) = 2.

  • Root 8.485281374
  • Exact form 6√2
  • Perfect power? No

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.