Question

3 /sqrt3-11 rationalize the denominator

Answer 1

The solved expression is
`(3)/(√(3)-11)=-(3√(3)+33)/(118)`

Explanation:

Given expression is
`(3)/(√(3)-11)`

To rationalize the given expression as below :

`(3)/(√(3)-11)`

Multiply and divide the conjugate of denominator
`√(3)-11` is
`√(3)+11` we get

`=((3)/(√(3)-11)* √(3)+11)/(√(3)+11)`

`=(3(√(3)+11))/((√(3)-11)(√(3)+11))`

`=(3(√(3)+3(11))/((√(3))^2-11^2)` ( using the formula
`(a-b)(a+b)=a^2-b^2` )

`=(3√(3)+33)/(3-121)`

`=(3√(3)+33)/(-118)`

`=-(3√(3)+33)/(118)`

Therefore the solved expression is
`-(3√(3)+33)/(118)`

Therefore the given expression is
`(3)/(√(3)-11)=-(3√(3)+33)/(118)`.