What is the definition of a non perfect square?
I have never before heard of a non-perfect square but I suppose it would be any
non-zero number that is not the square of an integer.
People sometimes say "perfect square" to mean an integer that is a square of an integer - I think the "perfect" is redundant but if you do not think "square" is clear by itself, say "integer square."
What is the difference between finding the square root of a perfect square and the square root of a non perfect square?
28 is not a perfect square. A perfect square is an integer that is the square of another integer. 9 is a perfect square; it equal to 3 squared, or 3 X 3. Often, such numbers are called simply square numbers. While 28 is not a perfect square, it is a square number in the sense that it has a square root. by definition, the square root of 28 times itself equals 28.
Well, the basic idea is that every positive number is the square of some number. For example, 2 is the square of a number known as the square root of 2; 3 is the square of a number known as the square root of 3; etc. The "perfect squares" are the squares of integers. That would make all other numbers "non-perfect squares", though this term is not usually used in practice.
True. By definition, a prime number is divisible by one and by itself. Also by definition, a perfect square has at least an additional pair of factors - it's square root. Therefore a prime number could never be a perfect square. One exception that might come to mind in this case is the number one. One however, is not considered a prime number, and thus does not conflict with this rule.
"Still" implies that the original number is a square number. In that case, the answer is as follows: There is no number such that it is a perfect sqiuare and that the number increased (or decreased) by 10 is also a perfect square. And if you do not limit it to perfect square then every non-negative number is a square with the number that is 10 more also being a square.
A perfect square trinomial is looking for compatible factors that would fit in the last term when multiplied and in the second term if added/subtracted (considering the signs of each polynomials). * * * * * A simpler answer is: write the trinomial in the form ax2 + bx + c. Then, if b2 = 4ac, it is a perfect square.