How this calculation works
When the input is itself a square, the two square bounds coincide. The same rule applies independently to cubes.
THE FORMULA
Use floor and ceiling of √n and ∛n, then square or cube themA worked example
30 lies between 25 and 36 for squares and between 27 and 64 for cubes.
Good to know
Use a nonnegative whole number.
Reference: OpenStax Prealgebra (opens in a new tab) ↗
Read the result
Find the perfect squares and cubes on either side of an integer and test whether it is already one.
The primary result is labeled “Square below or equal”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Use a nonnegative whole number.
For a related exercise, try the fraction calculator.
A few questions, answered
How can I check the default inputs by hand?
30 lies between 25 and 36 for squares and between 27 and 64 for cubes.
Which rule does this calculator apply?
Use floor and ceiling of √n and ∛n, then square or cube them