Question

What is the smallest natural number, which, when added to the difference of the squares of 17 and 13, gives a perfect square?

• A. 3
• B. 9
• C. 1
• D. 5

Answer 1

The correct option is C 1

Square of 17 = 289
Square of 13 = 169

Let's find the difference of the squares of 17 and 13.

${17}^2–{13}^2$
$=289–169$
$=120$

As we know, the nearest square after 120 is 121, which is a square of 11.

$120+1=121={11}^2$

Hence 1 is added to make it a perfect square.