Question

find the geometric mean of 8 and 28.
the geometric mean is
(there is a calculator interface shown with numbers 0 - 9 and operation symbols like ×, ÷, etc.)

Explanation:

Step1: Recall the formula for geometric mean

The formula for the geometric mean of two numbers \(a\) and \(b\) is \(\sqrt{ab}\). Here \(a = 8\) and \(b=28\).

Step2: Calculate the product \(ab\)

\(ab=8\times28 = 224\)

Step3: Find the square - root of the product

\(\sqrt{224}=\sqrt{16\times14}\)
Since \(\sqrt{16\times14}=\sqrt{16}\times\sqrt{14}\) and \(\sqrt{16} = 4\), we have \(\sqrt{224}=4\sqrt{14}\approx4\times3.742 = 14.968\approx15\)

Answer:

\(4\sqrt{14}\approx15\)