Question

Two consecutive perfect squares have a difference of $99$. what is the value of the larger perfect square?

Answer 1

Answer:

2500

Step-by-step explanation:

Let the first square number be $x^2$ then the next square number is $(x+1)^2$.

The difference between these two consecutive numbers is 99.

This implies that:

$(x+1)^2-x^2=99$

We expand to get:

$x^2+2x+1-x^2=99$

Simplify:

$2x=99-1$

$2x=98$

Divide both sides by 2

$x=49$

Therefore the value of the larger perfect number is

$(49+1)^2=50^2=2500$.