Hi Uday,
Solving the cubic eqn is the only proven method. I will advise to do the same. For this question, in particular, you can also use trial and error method. x needs to be a positive integer. So the resultant is 484. We know that 7^3=343 and 8^3=512. This means that x will be less than or equal to 7. Then try the values. Hope this helps.

Hi Rittu,
The number 484 in decimal system is 3414 in some base x.
To convert (3414) base x to decimal system, we can write it as-
3 X x^3 + 4 X x^2 + 1 X x + 4 X x^0 which is equal to 484.
Hope this helps.

Hi,
The second line describes decimal to base conversion.
Number 4 is present in the base representation. Hence, the base must be greater than 4. Start with 5 and check by substituting in equation described in the second line.

Hi Atulya,
The product of two numbers will always be the same in any number system. Only their representations will change according to the base system.
Hope that answers your query.

My question is that you have considered 44 and 11 as in Base 10 while the question seems to say that 44 and 11 have been taken in Base B.If Base is taken as 5, 44 and 11 will become 24 and 6 in Decimal and their product will become 144 and not 484.

Hii Atulya,
Sorry for the misunderstanding.
The question was indeed ambiguous. However, we have rectified it.
Feel free to ask if you have any further queries.