Question

Answer 1

C= \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{2}.\sqrt{3}+\sqrt{2}.\sqrt{4}+\sqrt{4}.\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

C= \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{2}.\sqrt{3}+\sqrt{2}.\sqrt{4}+2.\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

C= \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{2}.\sqrt{3}+\sqrt{2}.\sqrt{4}+\sqrt{2}.\sqrt{2}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

C= \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{2}.\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

C=\(\dfrac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)\left(\sqrt{2}+1\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

C= \(\sqrt{2}+1\)