Smallest number 3 Solution

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What is the smallest number which is both a cube and a square?

Solution:

Both 0 and 1 are technically both cubes and squares. They are known as self cubes and self squares, meaning that they are themselves squared and themselves cubed 0² = 0, 0³= 0, 1² = 1, 1³= 1.

The next smallest number which is both a square and a cube is 64 (4³ and 8²).

The easiest way to solve this problem is to make a list of cubes and check each to see whether it is also a square. Because the solution is the third whole number greater than 1 it does not take a long time.