Question 1185469


the least whole number that must be added to {{{1122}}} to get the perfect square number

{{{x+1122=x^2}}}

{{{x^2-x=1122}}} ....complete square

{{{x^2-x+b^2-b^2=1122 }}}

{{{(x^2-x+b^2)-b^2=1122}}} ..........{{{b=1/2}}}

{{{(x - 1/2)^2 - 1/4=1122}}}

{{{(x - 1/2)^2 =1122+1/4}}}

{{{(x - 1/2)^2 =4489/4}}}

{{{x - 1/2 =sqrt(4489/4)}}}

{{{x - 1/2 =67/2}}}

{{{x  =67/2+1/2}}}

{{{x  =68/2 }}}

{{{x=34}}}

check:

{{{34+1122=1156=34^2}}}