Question

The sum of a natural number and its positive square root is 132. Find the number.

Answer 1

Let the required natural number be x.

According to the given condition, 

`x + sqrt(x) = 132` 

Putting `sqrt(x) = y` or x = y², we get  

y² + y = 132 

⇒ y² + y – 132 = 0 

⇒ y² + 12y – 11y – 132 = 0 

⇒ y(y + 12) – 11(y + 12) = 0 

⇒ (y + 12)(y – 11) = 0 

⇒ y + 12 = 0 or y – 11 = 0 

⇒ y = –12 or y = 11 

∴ y = 11   ...(y cannot be negative) 

Now, 

`sqrt(x) = 11` 

⇒ x = (11)²

⇒ x = 121 

Hence, the required natural number is 121.