How do you rationalize the denominator and simplify #1/ (1+sqrt2)#?

2 Answers
Jul 28, 2018

Answer:

#-1+sqrt2#

Explanation:

#"rationalise the denominator by multiplying the"#
#"numerator/denominator by the conjugate of the"#
#"denominator"#

#"the conjugate of "1+sqrt2" is " 1 color(red)(-)sqrt2#

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

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

Answer:

#\sqrt2-1#

Explanation:

Given that

#1/{1+\sqrt2}#

#=1/{\sqrt2+1}#

#={\sqrt2-1}/{(\sqrt2+1)(\sqrt2-1)}#

#={\sqrt2-1}/{(\sqrt2)^2-1^2}#

#={\sqrt2-1}/{2-1}#

#=\sqrt2-1#