Question

find the geometric mean when a = 5 and b = 8.
geometric mean = ?√
simplify your answer completely.

Explanation:

Step1: Recall geometric mean formula

The geometric mean of two numbers $a$ and $b$ is $\sqrt{a \times b}$.

Step2: Substitute given values

Substitute $a=5$, $b=8$: $\sqrt{5 \times 8}$

Step3: Calculate product inside root

$5 \times 8 = 40$, so we get $\sqrt{40}$

Step4: Simplify the radical

Factor 40 into $4 \times 10$: $\sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}$

Answer:

$2\sqrt{10}$