If for a particular day of the year, it happens that the sum of the date and square root of the month gives the square of the month, then the date is:?

Let the day be x and the month be y

so 0<x<31 and 0<y<12 and x, y ε N (x and y are natural no.s)

Now given condition tells us that

x+√y=y²

so we get x=√y [y√y - 1]

But x is a natural no. so y has to be a perfect square

Hence possible values of y=1, 4, 9

taking y=1 we get x=1(1x1-1)=0   but x cannot be 0 so y is not 1

taking y=9 we get x=3(3x9-1)=78 but x cannot be more that 31

hence only y=4 is correct and then x=2(2x4-1)=14

Hence the final anwer will be 14^th of April is the day that satisfies the given condtions.

Please approve if u like the answer.