If the eight-digit number 342x18y6 is divisible by 72, then what is the value of $$\sqrt{9x + y}$$ , for the largest value of y ?

given, 8 digit number = 342x18y6 is divisible by 72.

means, 342x18y6 is also divisible by 8 as well as 9.

we know, any number is divisible by 8 only if last three digits of that number is divisible by 8.

here last three digits = 8y6

now tell me what is the possibility of y, then 8y6 will be divisible by 8.

of course, y = 1 , 5 and 9

so, we get y = 1 , 5 , 9

but question, say we have to find square root of (9x + y) for largest value of y.

so, take y = 9

now from divisibility of 9, any number is divisible by 9 only if sum of all digits is divisible by 9.

so, sum of digits = (3 + 4 + 2 + x + 1 + 8 + y + 6) = 24 + x + y

when we put y = 9 then, sum of digits = (33 + x ) , it is divisible by 9 when x = 3

so we get x = 3

now, y = 5 and x = 3

so, square root of (9x + y) = (9 × 3 + 9) = √(36) = 6