Calculate square root, cube root, and any nth root of any number instantly. Includes perfect square detection and step-by-step long division method.
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Type any positive number. Use the slider for quick exploration.
Square root is most common. Cube root is useful for volume problems.
Shows full precision, rounded value, and whether it is a perfect square.
Perfect squares are numbers whose square root is a whole integer: 1, 4, 9, 16, 25, 36... The square root of a negative number has no real solution — it is an imaginary number (denoted with i).
A perfect square is a number whose square root is a whole integer. Examples: 4 (√4=2), 9 (√9=3), 16, 25, 36, 49, 64, 81, 100.
√2 = 1.41421356... It is an irrational number — its decimal expansion never terminates or repeats. It appears in geometry as the diagonal of a unit square.
Not in real numbers. √−1 is defined as i (imaginary unit) in complex number mathematics. Even roots of negative numbers have no real solution.
Use the long division method: group digits in pairs from decimal, find the largest integer whose square fits, subtract and bring down the next pair, repeat. This calculator shows the result instantly.
The square root of 144 is 12, because 12 × 12 = 144. 144 is a perfect square. The square root of 2 is approximately 1.41421 (irrational — cannot be expressed as a simple fraction).