How do you simplify $1/(3+sqrt5)$ ?

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Answer 1 · 2018-04-07T13:29:05

$(3-sqrt5)/4$

Rationalize the denominator (radicals cannot be in the denominator) by multiplying the numerator and denominator by $3-sqrt5$

$1/(3+sqrt5)$

$(1*3-sqrt5)/((3+sqrt5)(3-sqrt5))$

$(3+sqrt5)(3-sqrt5)=9-3sqrt5+3sqrt5-sqrt25$

$9-3sqrt5+3sqrt5-sqrt25=9-5=4$

$(3-sqrt5)/4$

Answer 2 · 2018-04-07T13:30:29

$(3-sqrt(5))/4$

You can rationalise the denominator by multiplying by it’s conjugate.

$1/(3+sqrt(5))times(3-sqrt(5))/(3-sqrt(5))$

$=(3-sqrt(5))/(9-5)$

$=(3-sqrt(5))/4$

How do you simplify 1/(3+sqrt5) 1/(3+sqrt5) ?