Answer: 29, 38, 47, 56, 65, 74, 83, 92
Step-by-step explanation:
Let the two digit number be xy.
The tens value is x while the unit value is y
The number is then 10x+y
If it is written backwards, it is 10y+x
(10x+y) + (10y+x)
= 10x+y+10y+x
Collect like terms
10x+x+y+10y
= 11x+11y
= 11(x+y)
For 11(x+y) to be a perfect square, (x+y) must be equal to 11. So that we have
11*11=121
The combinations of x and y to give 11 when added, is from [1,2,3,4,5,6,7,8,9]
The possible combinations yield 29, 38, 47, 56, 65,74, 83 and 92
