What is the following quotient? 2/ square root 13 + square root 11 A. √(13) - 2 √(11) B. √(13) + √(11) / 6 C. √(13) + √(11) / 12 D. √(13) - √(11)

Question

What is the following quotient? 2/ square root 13 + square root 11

A.

`√(13) - 2 √(11)`
B.

`√(13) + √(11) / 6`
C.

`√(13) + √(11) / 12`
D.

`√(13) - √(11)`

Answer 1

Answer:D

Step-by-step explanation:Cause I said so

Answer 2

Given :
`(2)/(√(13)+√(11))`

`\mathrm{Multiply\:by\:the\:conjugate}\:(√(13)-√(11))/(√(13)-√(11))`

`=(2\left(√(13)-√(11)\right))/(\left(√(13)+√(11)\right)\left(√(13)-√(11)\right))`

\left(\sqrt{13}+\sqrt{11}\right)\left(\sqrt{13}-\sqrt{11}\right)

`\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}\left(a+b\right)\left(a-b\right)=a^2-b^2`

`a=√(13),\:b=√(11)`

`=\left(√(13)\right)^2-\left(√(11)\right)^2`

`\left(√(13)\right)^2-\left(√(11)\right)^2=13-11=2`

`=(2\left(√(13)-√(11)\right))/(2)`

`\mathrm{Divide\:the\:numbers:}\:(2)/(2)=1`

`=√(13)-√(11)`

Therefore, correct option is
`D.\\√(13) - √(11)`