Question

The difference of two perfect squares is a perfect square. If true then enter 1 and if false then enter 0.

Answer 1

Hint:
Consider two natural numbers and square them. Find the difference by subtracting the smaller number from the bigger number.

Complete step by step solution:
Let us consider two numbers here, 5 and 6.
The perfect square of 5 is $5^2=25$
The perfect square of 6 is $6^2=36$
Now, the bigger number here is 36, while the smaller number is 25.
The difference between them can be obtained by subtracting the smaller number from the bigger number.
Thus, the difference between the two perfect squares is 36-25=11
The square root of the difference of the squares of 5 and 6 is $\sqrt {11}$
The square root is not a natural number. It is not a perfect square.

Hence, it can be said that the difference between two perfect squares is not a perfect square.

Note:
A perfect square is a number, from a given number system, that can be expressed as the square of a number from the same number system. In the given sum, the difference of two perfect squares can be found out by considering any two natural numbers and subtracting the smaller number from the larger number. If the square root of the difference is a natural number, then it can be said that the difference of two perfect squares is a perfect square, but from the above sum, it is quite evident that the difference of two perfect squares is not a perfect square. Students need to conceptually understand the sum, before solving it. After understanding, the sum can be solved easily.