Chapter 8.1, Problem 46PPS

To determine

Whether the statement is always, sometime or never true.

Answer to Problem 46PPS

Always true.

Explanation of Solution

Given:

The given statement is:

The geometric mean of two perfect squares is a positive integer

Calculation:

Let m and n be the positive integer. The square of the numbers will be $m^2\text{ and }{n}^2$

Therefore,

  $\begin{array}{l}x=\sqrt{ab}\\ x=\sqrt{m^2\left(n^2\right)}\\ x=\sqrt{m^2{n}^2}\\ x=mn\end{array}$

The given statement is always true.