Question 56
(POL 5) Let $a$ and $b$ be two natural numbers that have an equal number $n$ of digits in their decimal expansions. The first $m$ digits (from left to right) of the numbers $a$ and $b$ are equal. Prove that if $m \gt n/2$, then
$$ a^{1/n}-b^{1/n} \lt \frac1n. $$
$$ a^{1/n}-b^{1/n} \lt \frac1n. $$