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

Puzzles and Curious Problems by Henry Ernest Dudeney: $84$

Find the Cube

A number increased by its cube is $592 \, 788$.

What is that number?

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.

$\blacksquare$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $84$. -- Find the Cube