For n to be a perfect square n = m2 where m can have one of the values 1, 2, 3, ...
1, 2, 3, ... are the counting numbers.
There are an infinite number of counting numbers, so there are an infinite number of perfect squares (n = m2).
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you can multiply two whole numbers together to get that. if you use graph paper, you could make a perfect square. the area of that square is called a perfect square because you can make a perfect square using that many units as the area. for example 4x4=16, so 16 would be the perfect square.
There is no limit to the number of perfect squares. To find a perfect square, you simply need to pick a number and square it. E.g. 7^2=49, so 49 is a perfect square. As there is infinitely many numbers to pick, and as the larger a number the larger it's square, there are infinitely many perfect squares and they just keep on getting larger!
The square root of a perfect square is a whole number. Example sqrt(36) = 6 so 36 is a perfect square Example sqrt(25) = 5 so 25 is a perfect square Example sqrt(8)= 2.828 which is not whole so 8 is not a perfect square
51 is not a perfect square. 72 = 49 82 = 64 51 is between 49 and 64 so its square root is 7+a bit, and it is not a perfect square.
no, 12 squared is 144 and 13 squared is 169. so no it is not a perfect square