Question

find the geometric mean when $a = 5$ and $b = 12$.
geometric mean = $?\sqrt{\square}$
simplify your answer completely.

Explanation:

Step1: Recall geometric mean formula

For two numbers $a$ and $b$, geometric mean = $\sqrt{a \times b}$

Step2: Substitute given values

Substitute $a=5$, $b=12$: $\sqrt{5 \times 12}$

Step3: Multiply inside the square root

$\sqrt{60}$

Step4: Simplify the radical

$\sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2\sqrt{15}$

Answer:

$\sqrt{60}$ or $2\sqrt{15}$