Question

The mean proportional between $(3+\sqrt{2})and(12-\sqrt{32})$ is

• A. $\sqrt{7}$
• B. $2\sqrt{7}$
• C. 6
• D. $\frac{15-3\sqrt{2}}{2}$

Answer 1

The correct option is B $2\sqrt{7}$

Required mean proportional $=\sqrt{(3+=\sqrt{2})(12-=\sqrt{32})}=\sqrt{36+12\sqrt{2}-3\sqrt{32}-\sqrt{64}}=\sqrt{36+12\sqrt{2}-3\sqrt{16\times 2}-8}=\sqrt{28+12\sqrt{2}-12\sqrt{2}}=\sqrt{28}=\sqrt{4\times 7}=2\sqrt{4}$