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Shrikant

· started a discussion

· 1 Months ago

Roots (Question:109807.0)

Explain.....??

Question:
Find the value of \(\cfrac{1}{3-\sqrt{8}}-\cfrac{1}{\sqrt[]{8}-\sqrt{7}}+\cfrac{1}{\sqrt[]{7}-\sqrt{6}}-\cfrac{1}{\sqrt[]{6}-\sqrt{5}}+\cfrac{1}{\sqrt[]{5}-2}\)
Options:
A) 0
B) 1
C) 5
D) 6
Solution:
\(\cfrac{1}{3-\sqrt{8}} - \cfrac{1}{\sqrt{8}-\sqrt{7}}+\cfrac{1}{\sqrt{7}-\sqrt{6}}-\cfrac{1}{\sqrt{6}-\sqrt{5}}+\cfrac{1}{\sqrt{5}-2}\) 

\(\cfrac{1}{\sqrt{9}-\sqrt{8}} - \cfrac{1}{\sqrt{8}-\sqrt{7}}+\cfrac{1}{\sqrt{7}-\sqrt{6}}-\cfrac{1}{\sqrt{6}-\sqrt{5}}+\cfrac{1}{\sqrt{5}-\sqrt{4}}\)

Rationalized

\(\Rightarrow\left ( \cfrac {1}{\sqrt{9}-\sqrt{8}}\times\cfrac{\sqrt{9}+\sqrt{8}}{\sqrt{9}+\sqrt{8}} \right )-\) \(\left ( \cfrac {1}{\sqrt{8}-\sqrt{7}}\times\cfrac{\sqrt{8}+\sqrt{7}}{\sqrt{8}+\sqrt{7}} \right )+\) \(\left ( \cfrac {1}{\sqrt{7}-\sqrt{6}}\times\cfrac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}} \right )\) \(-\left ( \cfrac {1}{\sqrt{6}-\sqrt{5}}\times\cfrac{\sqrt{6}+\sqrt{5}}{\sqrt{6}+\sqrt{5}} \right )+\) \(\left ( \cfrac {1}{\sqrt{5}-\sqrt{4}}\times\cfrac{\sqrt{5}+\sqrt{4}}{\sqrt{5}+\sqrt{4}} \right )\) 

\(\Rightarrow \sqrt{9}+\sqrt{8}-\sqrt{8}-\sqrt{7}+\sqrt{7}+\sqrt{6}-\sqrt{6}-\sqrt{5}+\sqrt{5}+\sqrt{4}\)

\(\Rightarrow \sqrt{9}+\sqrt{4}\Rightarrow3+2=5\)

Knowledge Expert

· commented

· 1 Months ago

Dear Student,
We first converted all the terms in form of roots, ie 3 = root 9 and 2 = root 4
Now rationalize each term and then follow the add/subtract operations as given in the question.
Given solution is right , you can refer that.

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