Question

find the geometric mean of 5 and 20.
the geometric mean is \boxed{}.
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall the formula for geometric mean

The geometric mean of two numbers \(a\) and \(b\) is given by \(\sqrt{ab}\).

Step2: Substitute the values of \(a = 5\) and \(b = 20\)

We have \(ab=5\times20 = 100\). Then the geometric mean is \(\sqrt{100}\).

Step3: Simplify the square root

\(\sqrt{100}=10\)

Answer:

10