Question

Find the geometric mean of 2 Square root of 6 and 3 square root of 6

Answer 1

Option B:

Geometric mean of $2 \sqrt{6} \ \text { and } \ 3 \sqrt{6}$ is 6.

Solution:

Given data:

$2 \sqrt{6} \ \text { and } \ 3 \sqrt{6}$

Geometric Mean is a average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc.

Let us multiply $2 \sqrt{6} \ \text { and } \ 3 \sqrt{6}$.

$2 \sqrt{6} \times 3 \sqrt{6}=2\times 3\times \sqrt{6} \times \sqrt{6}$

                  = 6 × 6

                  = 36

Now, taking square root for the product.

$\sqrt{2 \sqrt{6} \times 3 \sqrt{6}}=\sqrt{36}$

                     = $\sqrt{6^2}$

                     = 6

Geometric mean of $2 \sqrt{6} \ \text { and } \ 3 \sqrt{6}$ is 6.

Option B is the correct answer.