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(sqrt(5))/(sqrt(3)+sqrt(2))-(3sqrt(3))/(...

`(sqrt(5))/(sqrt(3)+sqrt(2))-(3sqrt(3))/(sqrt(5)+sqrt(2))+(2sqrt(2))/(sqrt(5)+sqrt(3))` is equal to :

A

0

B

`root(2)(15)`

C

`root(2)(10)`

D

`root(2)(6)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(sqrt(5))/(sqrt(5)+sqrt(2))-(3sqrt(3))/(sqrt(5)+sqrt(2))+(2sqrt(2))/(sqrt(5)+sqrt(3))`
`=(sqrt(5)(sqrt(3)-sqrt(2)))/((sqrt(3)+sqrt(2))(sqrt(3)-sqrt(2)))-(3sqrt(3)(sqrt(5)-sqrt(2)))/((sqrt(5)+sqrt(2))(sqrt(5)-sqrt(2)))`
`=(2sqrt(2)(sqrt(5)-sqrt(3)))/((sqrt(5)+sqrt(3))(sqrt(5)-sqrt(3)))`
`=(sqrt(15)-sqrt(10))/1-(3sqrt(15)-3sqrt(6))/3+(2sqrt(10)-2sqrt(6))/2`
`=sqrt(15)-sqrt(10)-sqrt(15)+sqrt(6)+sqrt(10)-sqrt(6)`
`=0`
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