what dose it mean to say that a numbers is a perfect square
To say that a number is a perfect square means that the number can be expressed as the product of an integer multiplied by itself. For example, 4 is a perfect square because it can be expressed as 2 multiplied by 2, which is written as 2^2. Similarly, 9 is a perfect square because it can be expressed as 3 multiplied by 3, or 3^2.
To determine whether a given number is a perfect square, you can take the square root of the number and check if the result is an integer. If the square root is an integer, then the number is a perfect square. If the square root is not an integer, then the number is not a perfect square.
For example, if we want to check whether 16 is a perfect square, we can take the square root of 16, which is 4. Since 4 is an integer, we can conclude that 16 is a perfect square.
Similarly, if we want to check whether 17 is a perfect square, we can take the square root of 17, which is approximately 4.123105625617661. Since 4.123105625617661 is not an integer, we can conclude that 17 is not a perfect square.