Question 59
The value of $$(1-\sqrt{2})+(\sqrt{2}-\sqrt{3})+(\sqrt{3}-\sqrt{4})+.....+(\sqrt{15}-\sqrt{16})$$ is
Solution
Expression : $$(1-\sqrt{2})+(\sqrt{2}-\sqrt{3})+(\sqrt{3}-\sqrt{4})+.....+(\sqrt{15}-\sqrt{16})$$
= $$1 + (-\sqrt{2}+\sqrt{2})+(-\sqrt{3}+\sqrt{3})+.....+(-\sqrt{14}+\sqrt{14})+(-\sqrt{15}+\sqrt{15})-\sqrt{16}$$
= $$1-\sqrt{16}=1-4=-3$$
=> Ans - (C)
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