Question

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Answer 1

Answer:

C) 3

Step-by-step explanation:

Sir i am not sure so pls don't repot

Answer 2

Answer:

(B) 2 is the right answer ✔

Step-by-step explanation:

Corrected Question :

$\mathrm{S = \dfrac{1}{\sqrt1+\sqrt4} + \dfrac{1}{\sqrt4 + \sqrt7} + \dfrac{1}{\sqrt7 + \sqrt{10}} + ... + \dfrac{1}{\sqrt{46} + \sqrt{49}}}$

To find :

The Value of S.

Solution :

$\longmapsto \mathrm{S = \dfrac{1}{\sqrt1+\sqrt4} + \dfrac{1}{\sqrt4 + \sqrt7} + \dfrac{1}{\sqrt7 + \sqrt{10}} + ... + \dfrac{1}{\sqrt{46} + \sqrt{49}}}$

Rationalizing each term, we get,

$\implies \mathrm{S = \dfrac{1}{\sqrt1+\sqrt4} \times \dfrac{\sqrt4 - \sqrt1}{\sqrt4 - \sqrt1} + \dfrac{1}{\sqrt4 + \sqrt7} \times \dfrac{\sqrt7 - \sqrt4}{\sqrt7 - \sqrt4}} +\\\\ \mathrm{\dfrac{1}{\sqrt7 + \sqrt{10}}\times \dfrac{\sqrt{10} - \sqrt7}{\sqrt{10} - \sqrt7} + ... + \dfrac{1}{\sqrt{46} + \sqrt{49}}\times \dfrac{\sqrt{49} - \sqrt{46}}{\sqrt{49} + \sqrt{46}}}$

$\implies \mathrm{S = \dfrac{\sqrt4-\sqrt1}{4-1} + \dfrac{\sqrt7 - \sqrt4}{7-4} + \dfrac{\sqrt{10} - \sqrt7}{10-7} + ... + \dfrac{\sqrt{49} - \sqrt{46}}{49-46}}$

$\implies \mathrm{S = \dfrac{\sqrt4-\sqrt1}{3} + \dfrac{\sqrt7 - \sqrt4}{3} + \dfrac{\sqrt{10} - \sqrt7}{3} + ... + \dfrac{\sqrt{49} - \sqrt{46}}{3}}$

$\implies \mathrm{S = \dfrac{1}{3} \Big(\sqrt4-\sqrt1 + \sqrt7 - \sqrt4 + \sqrt{10} - \sqrt7+ ... + \sqrt{49} - \sqrt{46}\Big)}$

$\implies \mathrm{S = \dfrac{1}{3} \Big(\cancel{\sqrt4}-\sqrt1 + \cancel{\sqrt7} - \cancel{\sqrt4} + \cancel{\sqrt{10}} - \cancel{\sqrt7}+ ... + \sqrt{49} - \cancel{\sqrt{46}}\Big)}$

$\implies \mathrm{S = \dfrac{1}{3} \Big( \sqrt{49} - \sqrt1 \Big)}$

$\implies \mathrm{S = \dfrac{1}{3} \Big( 7 -1\Big)}$

$\implies \mathrm{S = \dfrac{1}{\not 3} \Big( \not 6^2\Big)}$

$\implies \mathrm{S = 2}$

$\therefore \underline{\boxed{\Large{\textbf{S = 2}}}}$

Hence, Option (B)2 is the right answer

Hope it helps!!