0, 1
To be both a square and a cube, the number has to be a sixth power. You don't need to calculate though, since 06=0 and 16=1.
The next 2 sixth powers are 26=64 and 36=729.
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Very rarely. Square roots are only whole numbers for perfect squares.
None, although "perfect square" tends to be used for whole numbers.
perfect squares
They are the perfect squares.
How about 150*6 = 900 which is a perfect square because 30*30 = 900