Henry Ernest Dudeney/Puzzles and Curious Problems/84 - Find the Cube/Solution

by : $84$

 * Find the Cube

Solution

 * $84$

Proof
We are looking for $n$ such that:
 * $n^3 + n = 592 \, 788$

First we see that $\sqrt [3] {592 \, 788}$ is approximately $84 \cdotp 00...$

We calculate $84^3$ and get:
 * $84^3 = 592 \, 704$

and see that:
 * $84 + 592 \, 704 = 592 \, 788$

and our task is complete.