Powers and Roots Practice Test 4

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Question : 13 of 40

Marks: +1, -0

The value of

3+1/{√4+√5}+1/{√5+√6}+1/{√6+√7}

+1/{√7+√8}+1/{√8+√9}

is equal to:

4
3
2
$3 -√8$

Solution:

1/{√4+√5}=1/{√4+√5}×{√4-√5}/{√4-√5}

={√4-√5}/{(√4)^2-(√5)^2}

={ √5-√4}

Similarly,

1/{√5+√6}=√6-√5

and so on ….
Now,

3+√5-√4+√6+√5+√7

-√6+√8-√7+√9-√8

=3-√4+√9

=3-2+3=4

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