Which of the following relation is CORRECT?
I. $$(\sqrt{15}+\sqrt{7})<(2\sqrt{22})$$
II. $$(\sqrt{17}+\sqrt{5})<(\sqrt{20}+\sqrt{2})$$

I : $$(\sqrt{15}+\sqrt{7})<(2\sqrt{22})$$

Squaring both sides, we get :

L.H.S. = $$(\sqrt{15}+\sqrt{7})^2=15+7+2\sqrt{105}=(22+2\sqrt{105})\approx(22+2\times10)=42$$

R.H.S. = $$(2\sqrt{22})^2=88$$

Thus, L.H.S. < R.H.S., which is correct.

II : $$(\sqrt{17}+\sqrt{5})<(\sqrt{20}+\sqrt{2})$$

Squaring both sides, we get :

L.H.S. = $$(\sqrt{17}+\sqrt{5})^2=17+5+2\sqrt{85}=(22+2\sqrt{85})$$

R.H.S. = $$(\sqrt{20}+\sqrt{2})^2=20+2+2\sqrt{40}=(22+2\sqrt{40})$$

$$\because$$ $$\sqrt{85}>\sqrt{40}$$, then L.H.S. > R.H.S.

Thus, only I is correct.

=> Ans - (A)