How do you simplify $sqrt7/(sqrt11+3)$ ?

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Answer 1 · 2016-03-15T16:38:50

$(sqrt7)/(sqrt11+3)=(sqrt77-3sqrt7)/(2)$

$(sqrt7)/(sqrt11+3)=(sqrt7*(sqrt11-3))/((sqrt11+3)(sqrt11-3))$

$color(red)((a-b)(a+b)=a^2-b^2)$

$(sqrt7)/(sqrt11+3)=((sqrt7)*(sqrt11-3))/((sqrt11)^2-3^2)$

$(sqrt7)/(sqrt11+3)=((sqrt7)*(sqrt11-3))/(11-9)$

$(sqrt7)/(sqrt11+3)=((sqrt7)*(sqrt11-3))/(2)$

$(sqrt7)/(sqrt11+3)=(sqrt77-3sqrt7)/(2)$

How do you simplify sqrt7/(sqrt11+3)sqrt7/(sqrt11+3)?