How do you simplify 6/4+ Square root of 2?

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Answer 1 · 2015-05-31T18:56:54

To simplify $6/(4+sqrt(2))$ multiply numerator (top) and denominator (bottom) by the conjugate $(4-sqrt(2))$ ...

$6/(4+sqrt(2))$

$= 6/(4+sqrt(2))*(4-sqrt(2))/(4-sqrt(2))$

$= (6(4-sqrt(2)))/(4^2-sqrt(2)^2)$

$=(6(4-sqrt(2)))/(16-2)$

$=(6(4-sqrt(2)))/14$

$=(3(4-sqrt(2)))/7$

$=(12-3sqrt(2))/7$