Several ways of doing it.
One is by Chakans method, provided you know your times tables and the ones that result in squares ie 2x2,3x3,4x4 etc. I'm not sure how much of that is taught anymore at primary schools. We had to memorise upto the 12 times tables when I was a kid and be able to answer any of them during mental tests each morning.
Another if you are unsure is a quick deduction process, ie
If the answer has to be a two digit number it must be between 10 and 99 and since they say it's an odd, its square root has got to be either 1,3,5,7 or 9.
Why? Well even numbers multiplied together always result in an even answer and we want an odd one, and any larger whole number than 9 squared would result in 3 digit answers ie 11x11=121.
And if the product result has to be 8, it must also be a answer less than 90 as otherwise the product would be greater than 8.
So, we are looking for an answer that is less than 90 and the nearest number from our potential candidate list from above to get that result is 9, and sure enough, 9x9=81, and the product of the digits in 81 is 8.