How do you simplify $7/(5+sqrt3)$ ?

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Answer 1 · 2017-03-31T09:22:29

$=35/22-(7sqrt3)/22$

You must know that the conjugate of an irrational number of the type
$a+sqrtb$ is given by $a-sqrtb$ and that of $a-sqrtb$ is given by $a+sqrtb$ .

$7/(5+sqrt3)$

(multiplying and dividing by conjugate of $5+sqrt3$ )

$= 7/(5+sqrt3)*(5-sqrt3)/(5-sqrt3)$

$= (7(5-sqrt3))/(5^2-(sqrt3)^2)$

$=(7(5-sqrt3))/22$
$=35/22-(7sqrt3)/22$

Answer 2 · 2017-03-31T09:33:42

Rationalise the denominator by multiplying by the conjugate surd.

$7/(5+sqrt3)$ = $7/(5 + sqrt3) * (5-sqrt3)/(5-sqrt3)$

= $[7(5-sqrt3)]/[(5^2)-(sqrt3)^2]$

= $(35 - 7sqrt3)/(25 - 3)$

= $(35 - 7sqrt3)/22$

How do you simplify 7/(5+sqrt3)7/(5+sqrt3)?