Chapter 8.1, Problem 47PPS

To determine

Whether the statement is always, sometime or never true.

Answer to Problem 47PPS

Sometimes true.

Explanation of Solution

Given:

The given statement is:

The geometric mean of two positive integers is an integer

Calculation:

Let 6 and 24 be the positive integer. Therefore,

  $\begin{array}{l}x=\sqrt{ab}\\ x=\sqrt{6\left(24\right)}\\ x=\sqrt{144}\\ x=12\end{array}$

And let 2 and 3 be the positive integer. Therefore,

  $\begin{array}{l}x=\sqrt{ab}\\ x=\sqrt{2\left(3\right)}\\ x=\sqrt{6}\end{array}$

The given statement is sometimes true.