How do you simplify #2/(1+sqrt2)#?

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Answer 1 · 2015-12-03T08:10:33

#=color(blue)(2sqrt2-2#

#2/(1+sqrt2)#

We simplify this expression by rationalising the denominator.

We multiply both the numerator and the denominator by the conjugate of the denominator which is

#=color(blue)(1-sqrt2#

So,
#2/(1+sqrt2) = (2*color(blue)((1-sqrt2)))/((1+sqrt2)*(color(blue)(1-sqrt2))#

We apply the property :

#color(blue)((a+b)(a-b)=(a^2-b^2)#, to the denominator.

#= (2 * 1-2 * sqrt2)/((1^2 - (sqrt2)^2)#

#= (2 -2sqrt2)/((1 - 2)#

#= (2 -2sqrt2)/(-1 #

#=color(blue)(2sqrt2-2#