what does it mean to say that a number is a perfect square? give one example of a number that is a perfect square and one that is not. explain your examples, define the term perfect square, and provide examples and explain why each is or is not a perfect square.
A perfect square is a number that can be obtained by multiplying a whole number by itself. For example, 9 is a perfect square because it can be obtained by multiplying 3 by 3 (3x3=9). On the other hand, 10 is not a perfect square because it cannot be obtained by multiplying any whole number by itself.
Another example of a perfect square is 25, which can be obtained by multiplying 5 by 5 (5x5=25). Similarly, 36 is a perfect square because it can be obtained by multiplying 6 by 6 (6x6=36).
In contrast, 17 is not a perfect square because it cannot be obtained by multiplying any whole number by itself. It is a prime number, which means it is only divisible by 1 and itself.
Overall, the term perfect square refers to a number that is the product of a whole number multiplied by itself, and examples include 4, 16, 49, and 100. Numbers that cannot be obtained through this multiplication method are not perfect squares, such as 8, 15, and 21.
To say that a number is a perfect square means that the number can be expressed as the square of an integer, i.e., it is the result of multiplying a whole number by itself. In other words, a perfect square is a number that has an exact square root, resulting in a whole number.
Let me provide you with an example of a perfect square and a number that is not a perfect square:
Example 1: 25 is a perfect square because it can be expressed as 5 squared (5^2 = 25). The square root of 25 is 5, which is a whole number.
Example 2: 17 is not a perfect square because there is no whole number that can be multiplied by itself to give 17. The square root of 17 is an irrational number (approximately 4.123), indicating that it cannot be expressed as a ratio of two integers.
In summary, a perfect square is a number that can be obtained by squaring a whole number. If a number has an exact square root, resulting in a whole number, then it is a perfect square. Otherwise, if the square root is irrational, it is not a perfect square.