Question

The sum of a two digit number and the number obtained by reversing its digits is a sqare number how many such number are there

Answer 1

Let a be the first digit and b be the second digit.
value of the number is 10a+b .

value of the number obtained by reversing its digits is 10b+a

Their sum is
10a+b+10b+a = 11a+11b = 11(a+b)

For the sum to be the square of an integer, it must be true that
a+b=11 .
There are 4 possible combinations of digits adding to 11 :
2+9=11 ,
3+8=11 ,
4+7=11 , and
5+6=11 .s
Since we can make two 2-digit number out of each paiR
by changing the other of the digits,
there are 2*4=8 numbers that could be
the original 2-digit number