How do you simplify $3/ (6- sqrt 5)$ ?

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Answer 1 · 2018-03-13T10:20:49

$3/(6-sqrt 5) = 3/31 (6+sqrt 5)$

By rationalizing the denominator:

$3/(6-sqrt 5) xx (6+sqrt 5)/(6+sqrt 5)$

$= (3 xx (6+sqrt 5)) / (6^2 - (sqrt5)^2)$

$= (3xx(6+sqrt 5)) / (36-5)$

$= 3/31 (6+sqrt 5)$

Answer 2 · 2018-03-13T10:24:01

Multiply the numerator and denominator by the conjugate of the denominator and simplify

$3/(6-sqrt(5))$
$color(white)("XXX")=3/(6-sqrt(5)) * (6+sqrt(5))/(6+sqrt(5))$

$color(white)("XXX")=(3(6+sqrt(5)))/(6^2-(sqrt(5))^2)$

$color(white)("XXX")=(18+3sqrt(5))/(36-5)$

$color(white)("XXX")=(18+3sqrt(5))/31$

How do you simplify 3/ (6- sqrt 5)3/ (6- sqrt 5)?