Question

Find the cube root of $103823$.

Answer 1

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 $47$.