Question

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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 of a perfect square
_provide examples, and explain why each is or is not a perfect square.

Answer 1

A perfect square is a number that you can take the square root of and get a whole number

Example

\[\large \sqrt{9} = 3\] so we know that 3 is a perfect square...however if we have \[\large \sqrt{5}\] is that a whole number? no..so 5 is NOT a perfect square

in general, its easy to remember if you take EVERY number a square it...we will get a perfect square

1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16

1,4,9 and 16 are all examples of perfect squares

Answer 2

Examples of perfect squares

9
9 is a perfect square because it can be expressed as 3 * 3 (the product of two equal integers)
16
16 is a perfect square because it can be expressed as 4 * 4 (the product of two equal integers)
25
25 is a perfect square because it can be expressed as 5 * 5 (the product of two equal integers)
Non examples of perfect squares

8
8 is a not perfect square because you cannot express it as the product of two equal integers
5
5 is a not perfect square because it cannot be expressed as the product of two equal integers
7
7 is a not perfect square because you cannot express it as the product of two equal integers