If the value of 624 in the base 7 system is equal to 312 in the base k system, then find the value of $$k^2$$
Solution
To solve such questions, it is always advisable to convert the number first into decimal (base 10) and then analyse the result.
As per the question, we have 624 in base 7. To convert it into decimal, we do: 6$$\times\ $$ $$7^2$$ + 2$$\times\ $$ 7 + 4$$\times\ $$ 1, which is 312.
This is exactly what we have in the question, which means that the number is 312 in base 10.
Hence, $$10^2$$ = 100
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