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Question

Find the cube root of $$103823$$.


Solution

Here the units digit of $$103823$$ is $$3$$. If $$n^3 = 103823$$, then the units digit of $$n$$ must be $$7$$. 
Let us split $$103823$$ as $$103$$ and $$823$$. We observe that $$4^3 = 64 < 103 < 125 = 5^3$$. Hence

$$40^3 = 64000 < 103823 < 125000 = 50^3$$.
Hence $$n$$ must lie between $$40$$ and $$50$$. Since the units digit of $$n$$ is $$7$$, the only such number is $$47$$.

Mathematics

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