Question

What is the following quotient? 2/sqrt13+sqrt11

Answer 1

The correct Answer is D
`√(13) - √(11)`

Explanation:

Answer 2

Answer is
`√(13)-√(11)`

Explanation:

We need to divide

`(2)/(√(13)+√(11))`

For solving this, we need to multiply and divide the given term with the conjugate of
`{√(13)+√(11)`

The conjugate is:
`{√(13)-√(11)`

Solving

`=(2)/(√(13)+√(11)) *(√(13)-√(11))/(√(13)-√(11)) \\=(2(√(13)-√(11)))/((√(13)+√(11))(√(13)-√(11)))\\We\,\, know\,\, that\,\, (a+b)(a-b) = a^2-b^2\\=(2(√(13)-√(11)))/((√(13))^2-(√(11))^2)\\=(2(√(13)-√(11)))/(13-11)\\=(2(√(13)-√(11)))/(2)\\=√(13)-√(11)`

So answer is
`√(13)-√(11)`