Choose the correct relation(s) from the following: (i) \sqrt{6}+\sqrt{2}=\sqrt{5}+\sqrt{3} (ii) \sqrt{6}+\sqrt{2}<\sqrt{5}+\sqrt{3} (iii) \sqrt{6}+\sqrt{2}>\sqrt{5}+\sqrt{3}

Question 88

Choose the correct relation(s) from the following:
(i) $$\sqrt{6}+\sqrt{2}=\sqrt{5}+\sqrt{3}$$
(ii) $$\sqrt{6}+\sqrt{2}<\sqrt{5}+\sqrt{3}$$
(iii) $$\sqrt{6}+\sqrt{2}>\sqrt{5}+\sqrt{3}$$

Solution

$$\sqrt{2}$$ = 1.414

$$\sqrt{3}$$ = 1.732

$$\sqrt{5}$$ = 2.236

$$\sqrt{6}$$ = 2.449

=> $$\sqrt{2}$$ + $$\sqrt{6}$$ = 3.863

and $$\sqrt{5}$$ + $$\sqrt{3}$$ = 3.968

=> $$\sqrt{2}$$ + $$\sqrt{6}$$ < $$\sqrt{5}$$ + $$\sqrt{3}$$

Thus, (ii) is correct.

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