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Q: What is the smallest integer where the integer before it is a perfect square and the integer after it is a perfect cube?

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I have never before heard of a non-perfect square but I suppose it would be any non-zero number that is not the square of an integer. People sometimes say "perfect square" to mean an integer that is a square of an integer - I think the "perfect" is redundant but if you do not think "square" is clear by itself, say "integer square."

The smallest integer is 2.There is no smallest number. Dividing 1152 by any number of the form x = 1/(2k2) where k is an integer will result in a perfect square. Since there is no limit to how large k can be, there is no limit to how small x can be.

Find the square root of the number.Take the integer part of the answer.Square the integer part.Subtract this square from the original number.

an integer

90 is a not perfect square.

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its 81

6.

I have never before heard of a non-perfect square but I suppose it would be any non-zero number that is not the square of an integer. People sometimes say "perfect square" to mean an integer that is a square of an integer - I think the "perfect" is redundant but if you do not think "square" is clear by itself, say "integer square."

Yes it is.Since the square of an integer is called a perfect square, then the square root of a perfect square must be an integer.

A perfect square is a square of an integer (a whole number).

Find the square root of the number.Take the integer part of the answer.Square the integer part.Subtract this square from the original number.

The smallest integer is 2.There is no smallest number. Dividing 1152 by any number of the form x = 1/(2k2) where k is an integer will result in a perfect square. Since there is no limit to how large k can be, there is no limit to how small x can be.

The smallest integer is 11 but there is no smallest number! 0.11 is a smaller number and will give a perfect square. 0.0011 is smaller still, and 0.000011 even smaller. That sequence is endless!

an integer

Yes, a perfect square is a number that has an integer square root.

Given the prime factorization of an integer how can you determine if our integer is a perfect square?

90 is a not perfect square.

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