Question

directions: find the geometric mean of each pair of numbers.

1. 16 and 27
2. 5 and 36
3. 24 and 32
4. 8 and 48

Explanation:

Step1: Recall geometric mean formula

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

Step2: Solve for 16 and 27

$GM = \sqrt{16 \times 27} = \sqrt{432} = 12\sqrt{3}$

Step3: Solve for 5 and 36

$GM = \sqrt{5 \times 36} = \sqrt{180} = 6\sqrt{5}$

Step4: Solve for 24 and 32

$GM = \sqrt{24 \times 32} = \sqrt{768} = 16\sqrt{3}$

Step5: Solve for 8 and 48

$GM = \sqrt{8 \times 48} = \sqrt{384} = 8\sqrt{6}$

Answer:

1. $12\sqrt{3}$
2. $6\sqrt{5}$
3. $16\sqrt{3}$
4. $8\sqrt{6}$