when 123 is added to a perfect square number the new number so formed is also perfect square find - Maths - Squares and Square Roots

Question

when 123 is added to a perfect square number the new number so
formed is also perfect square find the square root of the new
number

Kalpalata Chakraborty · Accepted Answer

Let the perfect square number be x2 and new perfect sq number be y2
A/q, y2−x2=123=>(y+x)(y−x)=41 3∴y+x=41 (1)and
y−x=3 (2)Now adding (1) and (2), we get,y=22Putting the value
of y in (1),we get x=19 ∴The perfect sq numbers are 192,i e
361 and 222,i e 484

when 123 is added to a perfect square number the new number so formed is also perfect square. find the square root of the new number.