Question

Rationalise the denominator of root 2 -1 root 2+1​

Answer 1

$\frac{1}{\sqrt{a} +\sqrt{b} } =\frac{\sqrt{a} -\sqrt{b} }{(\sqrt{a} +\sqrt{b} )(\sqrt{a} -\sqrt{b} )} =\frac{\sqrt{a} -\sqrt{b} }{a-b}$

In other words, multiply same number on the numerator and the denominator in order to apply the identity $(a+b)(a-b)=a^2-b^2$.

$\frac{\sqrt{2} -1}{\sqrt{2} +1} =\frac{(\sqrt{2} -1)^2}{(\sqrt{2} +1)(\sqrt{2} -1)} =\frac{2-2\sqrt{2}+1}{2-1} =\frac{3-2\sqrt{2} }{1} =3-2\sqrt{2}$

The answer is $3-2\sqrt{2}$.