2 consecutive perfect squares differ by 999. What is the larger of these squares?

Guest Oct 26, 2019

#1**+1 **

**The larger perfect square = 500^2 =250,000**

**The smaller perfect square =499^2 =249,001**

**250,000 - 249,001 =999 - difference**

Guest Oct 26, 2019

#2**+2 **

x^{2} is the first number

(x + 1)^{2} is the second number

These numbers are consecutive.

(x+1)^{2} - x^{2 }= 999 (they differ by 999)

Expand (x+1)^{2 }, then simplify.

x^{2} + 2x + 1 - x^{2} = 999

2x + 1 = 999

x = 499

Bigger number is 499 + 1 = **500**

**This is how you solve these problems.**

CalculatorUser
Oct 26, 2019