Here we will answer the question: "Is 675 a square number?" You could also ask "Is 675 a perfect square?" Square number and perfect square mean the same thing.
Anyway, for 675 to be a square number, 675 must be the product of an integer multiplied by itself. In other words, the square root of 675 must equal a whole number (integer).
There is no integer that you can multiply by itself that will make 675. Furthermore, the square root of 675 is not an integer. Thus, 675 is NOT a square number.
The answer to the question: "Is 675 a square number?" is No.
The answer to the question: "Is 675 a perfect square?" is also No.
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