Question

what is the geometric mean of 2 and 6? (simplify your answer. 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 \(a = 2\) and \(b = 6\)

We substitute \(a = 2\) and \(b = 6\) into the formula: \(\sqrt{2\times6}\).

Step3: Simplify the expression inside the square root

Calculate \(2\times6 = 12\), so we have \(\sqrt{12}\).

Step4: Simplify the radical

We can simplify \(\sqrt{12}\) as \(\sqrt{4\times3}\), and since \(\sqrt{4}=2\), this becomes \(2\sqrt{3}\).

Answer:

\(2\sqrt{3}\)