A natural number m is called a perfect square number if it can be expressed as where n is also a natural number. For example, 4 is a perfect square number because it is a natural number and it can be expressed as and 2 is also a natural number.
We have a property
Can we easily find the value of using the above property?
If you want to recall what are perfect square numbers then please refer to my article on What are the perfect square numbers. This article asks a question that how many natural numbers lie between two consecutive perfect square numbers. You can also ask the same question as how many non-perfect square numbers lie between two consecutive perfect square numbers? Can we come up with a general formula for that?
If you take a look at sum of first n odd numbers, you can notice very interesting pattern.
1 = 1
1 + 3 = 4
"Pythagoras Theorem" How to find third side of right angled triangle when two other sides are given?
Pythagoras theorem states that "In a right angled triangles" square of hypotenuse is equal to sum of squares of other two sides.