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#