Question

Rationalizing the denominator :-
a) 1/(3+√2)
b) 6/(√5+√2​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

a) $\dfrac{1}{3+\sqrt2}$

Multiply as well as divide by 3 - $\sqrt2$

$\implies\dfrac{3-\sqrt2}{(3+\sqrt2)(3-\sqrt2)}\\\\\\\implies \dfrac{3-\sqrt2}{(3)^2-(\sqrt2)^2 }\\\\\\\implies \dfrac{3-\sqrt2 }{9-2}\\\\\\\implies \dfrac{3- \sqrt2}{7}$

b) $\dfrac{6}{\sqrt5 + \sqrt2}$

Multiply as well as divide by $\sqrt5 - \sqrt2$

$\dfrac{6(\sqrt5 - \sqrt2)}{(\sqrt5 + \sqrt2)(\sqrt5 - \sqrt2)}\\\\\\\implies \dfrac{6(\sqrt 5 - \sqrt2) }{( \sqrt5 )^2 - (\sqrt2)^2 } \\\\\\\implies \dfrac{ 6(\sqrt 5 -\sqrt2 )}{5-2}\\\\\\\implies \dfrac{6(\sqrt5 - \sqrt2)}{3}\\\\\\\implies 2(\sqrt5 -\sqrt 2 )$