The mean proportional between (18 + 10$$\sqrt{7}$$​) and (18 – 4$$\sqrt{7}$$​) is:

Correct option is A

Given:

Two numbers: 18 + 10$$\sqrt{7}$$​ and 18 - 4$$\sqrt{7}$$​​

Formula Used:

Mean Proportional = $$\sqrt{(a \times b)}$$​​

Solution: 

Mean Proportional = $$\sqrt{(18+10\sqrt7)(18 - 4\sqrt7)}$$ 

​$$=\sqrt{(18)^2-72\sqrt7+180\sqrt7-280)}\\ \ \\ =\sqrt{324 -280+108\sqrt7}\\ \ \\ =\sqrt{44+108\sqrt7}$$​​