Square root and cube root
Enter a number: I'll calculate its square root and cube root, tell you whether it's a perfect square or a perfect cube, and show the nearest perfect squares.
Non-exact values are rounded to six decimal places.
Perfect squares and perfect cubes: how to spot them
A perfect square is an integer that is the square of another integer (1, 4, 9, 16, 25, 36…); a perfect cube is the cube of an integer (1, 8, 27, 64, 125…). Here's a quick trick: in base ten, a perfect square can never end in 2, 3, 7 or 8. So 1372 or 253 can be ruled out at a glance, while a number ending in 0, 1, 4, 5, 6 or 9 needs to be checked — which is exactly what this tool does, also showing you which perfect squares your number falls between.
What square roots and cube roots are used for
The square root answers questions about areas and distances: a square room with an area of 200 sq ft has sides of √200 ≈ 14.14 ft, and the Pythagorean theorem uses it to find the hypotenuse. The cube root works on volumes: a cube-shaped tank holding 27 cubic feet has edges of ∛27 = 3 ft, and doubling a cube's volume only requires multiplying its side by ∛2 ≈ 1.26. Unlike the square root, the cube root also exists for negative numbers: ∛(−8) = −2.