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

2 Answers
Jim G.
Jul 28, 2018

-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

Harish Chandra Rajpoot
Jul 28, 2018

\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

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
15858 views around the world
You can reuse this answer
Creative Commons License