The value of 1-9 - -8 - 1-8 - -7 - 1-7 - -6 - 1-6 - -5 - 1-5 - -4 is equal to

The correct option is C 5 1√(9) √(8) = √(9) + √(8)(√(9) √(8))(√(9) + √(8)) = √(9) + √(8) 1√(8) √(7) = √(8) + √(7) and so on. ∴ Given ...

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Byju's Answer

Standard XII

Mathematics

Sum of n Terms

The value of ...

Question

The value of $\frac{1}{\sqrt{9} - \sqrt{8}} - \frac{1}{\sqrt{8} - \sqrt{7}} + \frac{1}{\sqrt{7} - \sqrt{6}} - \frac{1}{\sqrt{6} - \sqrt{5}} + \frac{1}{\sqrt{5} - \sqrt{4}}$ is equal to

0

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1

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5

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\frac{1}{3}

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Solution

The correct option is C $5$
$\frac{1}{\sqrt{9} - \sqrt{8}} = \frac{\sqrt{9} + \sqrt{8}}{(\sqrt{9} - \sqrt{8}) (\sqrt{9} + \sqrt{8})} = \sqrt{9} + \sqrt{8}$
$\frac{1}{\sqrt{8} - \sqrt{7}} = \sqrt{8} + \sqrt{7}$ and so on.
$∴$ Given expression is
$(\sqrt{9} + \sqrt{8}) - (\sqrt{8} + \sqrt{7}) + (\sqrt{7} - \sqrt{6}) - (\sqrt{6} + \sqrt{5}) + (\sqrt{5} + \sqrt{4})$
$= \sqrt{9} + \sqrt{4} = 3 + 2 = 5$

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Similar questions

$\frac{1}{(\sqrt{9} - \sqrt{8})} - \frac{1}{(\sqrt{8} - \sqrt{7})} + \frac{1}{(\sqrt{7} - \sqrt{6})} - \frac{1}{(\sqrt{6} - \sqrt{5})} + \frac{1}{(\sqrt{5} - \sqrt{4})}$ is equal to:

Q. What is the value of

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

Q. The value of

\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}}

is.

Q. The value of :

\frac{1}{\sqrt{9} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{1}}

is :

Q. Study the following number line and answer the questions that follow.
2 5 9 1 7 2 5 1 9 7 3 9 5 2 4 6 8 1 9 7 5 2 7 3 1 9 7 8 5 2 6 5 4 1 9 7 8 2 0 1 0 9 7 8 5 1 9 7 3 5 1 6 9 7 2 1 7 3 7 9 5 1

How many times is number 5 followed by 1 or 2, but not preceded by 8 ?

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The value of 1√9−√8−1√8−√7+1√7−√6−1√6−√5+1√5−√4 is equal to

The correct option is C 51√9−√8=√9+√8(√9−√8)(√9+√8)=√9+√81√8−√7=√8+√7 and so on.∴ Given expression is(√9+√8)−(√8+√7)+(√7−√6)−(√6+√5)+(√5+√4)=√9+√4=3+2=5

The value of $\frac{1}{\sqrt{9} - \sqrt{8}} - \frac{1}{\sqrt{8} - \sqrt{7}} + \frac{1}{\sqrt{7} - \sqrt{6}} - \frac{1}{\sqrt{6} - \sqrt{5}} + \frac{1}{\sqrt{5} - \sqrt{4}}$ is equal to