Question

rationalise the denominator :

$1 \div \sqrt{3 + \sqrt{2} }$
​

Answer 1

Step-by-step explanation:

${\small{\bold{ \dfrac{1}{\sqrt{3+\sqrt{2}}}}}}$

Rationalising the denominator

${\small{\tt{\implies{\dfrac{1}{\sqrt{3+\sqrt{2}}} × \dfrac{ \sqrt{3-\sqrt{2}}}{ \sqrt{3-\sqrt{2}}}}}}}$

${\small{\tt{\implies{\dfrac{\sqrt{3-\sqrt{2}}}{ \big(\sqrt{(3)^2-(\sqrt{2})^2} \big)^2}}}}}$

${\small{\tt{\implies{\dfrac{\sqrt{3-\sqrt{2}}}{9-2}}}}}$

${\small{\tt{\implies{\small{\tt{\underline{\boxed{\dfrac{\sqrt{3-\sqrt{2}}}{7}}}}}}}}}$