Between which two integers does \(57^3\) lie?

To find the range of integers between which \(57^3\) lies, we can calculate the value of \(57^3\).

\(57^3 = 57 \times 57 \times 57 = 185193\)

Therefore, \(57^3\) lies between 185192 and 185194.

So, \(57^3\) lies between the integers 185192 and 185194.

We can use the fact that \(a^3 < b^3\) if \(a < b\).

Since \(55^3 = 166,375\), we have \(57^3 > 166,375\).

Since \(58^3 = 175,616\), we have \(57^3 < 175,616\).

Therefore, \(57^3\) lies between \(166,375\) and \(175,616\).