Question 1180669


let a number be {{{n}}}

if the difference between a number and it’s positive square root is {{{12}}}, we have

{{{n-sqrt(n)=12}}}
{{{n-12=sqrt(n)}}}....square both sides
{{{(n-12)^2=(sqrt(n))^2}}}
{{{n^2-24n+144=n}}}
{{{n^2-24n+144-n=0}}}
{{{n^2-25n+144=0}}}
{{{n^2-25n+144=0}}}
{{{(n - 16) (n - 9) = 0}}}

solution: 

{{{(n - 16) = 0}}}=>{{{n=16}}}
{{{(n - 9) = 0}}}=>{{{n=9}}}

check which solution works

{{{n-sqrt(n)=12}}}=>{{{n=16}}}
{{{16-sqrt(16)=12}}}
{{{16-4=12}}}
{{{12=12}}}-> this solution works

{{{9-sqrt(9)=12}}}=>{{{n=9}}}
{{{9-3=12}}}
{{{6<>12}}}-> this solution does not work

so,  the number is  {{{16}}}