Question

your turn
find the geometric mean of the numbers. if necessary, give the answer in simplest radical form.

1. 6 and 24
2. 5 and 12

Explanation:

Define the geometric mean formula

The geometric mean of two positive numbers \(a\) and \(b\) is the positive square root of their product:

$$x = \sqrt{a \cdot b}$$

Calculate the geometric mean for Question 1

For the numbers \(6\) and \(24\):

$$x = \sqrt{6 \cdot 24}$$

$$x = \sqrt{144}$$

$$x = 12$$

Calculate the geometric mean for Question 2

For the numbers \(5\) and \(12\):

$$x = \sqrt{5 \cdot 12}$$

$$x = \sqrt{60}$$

Simplify the radical expression

To write \(\sqrt{60}\) in simplest radical form, find the largest perfect square factor of \(60\), which is \(4\):

$$x = \sqrt{4 \cdot 15}$$

$$x = 2\sqrt{15}$$

Answer:

Question 1

12

Question 2

\(2\sqrt{15}\)