Question

find the geometric mean of 4 and 9.
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 \(a = 4\) and \(b = 9\)

Substitute \(a = 4\) and \(b = 9\) into the formula: \(\sqrt{4\times9}\).

Step3: Simplify the expression

First, calculate the product inside the square root: \(4\times9 = 36\). Then, take the square root of 36: \(\sqrt{36}=6\).

Answer:

6