Find the mean proportional of (12 + 6√2) and (8 - 4√2).

Correct option is A

Given:
Mean proportional of $$(12 + 6\sqrt{2}) \text{and} (8 - 4\sqrt{2})$$​
Formula Used:
Mean Proportional of a and b is given by $$\sqrt {a × b}$$​​
Solution:
Substitute the values of $$a=(12 + 6\sqrt{2}) \text{and}\, b= (8 - 4\sqrt{2})$$​​
​$$\text{Mean Proportional} = \sqrt{(12 + 6\sqrt{2}) \times (8 - 4\sqrt{2})} \\\text{Mean Proportional} = \sqrt{12 \times 8 + 12 \times (-4\sqrt{2}) + 6\sqrt{2} \times 8 + 6\sqrt{2} \times (-4\sqrt{2})} \\\text{Mean Proportional} = \sqrt{96 - 48\sqrt{2} + 48\sqrt{2} - 48} \\\text{Mean Proportional} = \sqrt{48} \\\text{Mean Proportional} = 4\sqrt{3}$$​​