Question

plzz ans with whole process...plzzz....i will mark as brainliest but plz ans correctly with whole steps​

Answer 1

Answer:

$1 + \sqrt{5} -\sqrt{2} + \sqrt{10}$

Step-by-step explanation:

Given :

To rationalise the denominator,

$\frac{12}{3 + \sqrt{5} - 2\sqrt{2} }$

Solution :

$(\frac{12}{3 + \sqrt{5} - 2\sqrt{2}})(\frac{3 - \sqrt{5} - 2\sqrt{2}}{3 - \sqrt{5} - 2\sqrt{2}})$

⇒ $(\frac{12(3 - \sqrt{5} - 2\sqrt{2})}{(3 -2\sqrt{2})^2 -(\sqrt{5})^2}})$

⇒ $(\frac{12(3 - \sqrt{5} - 2\sqrt{2})}{(9 + 8 - 12\sqrt{2}- 5) }})$

⇒ $(\frac{12(3 - \sqrt{5} - 2\sqrt{2})}{(12 - 12\sqrt{2}) }})$

⇒ $(\frac{12(3 - \sqrt{5} - 2\sqrt{2})}{12(1 - \sqrt{2}) }})$

⇒ $(\frac{3 - \sqrt{5} - 2\sqrt{2}}{1 - \sqrt{2} }})$

⇒ $(\frac{3 - \sqrt{5} - 2\sqrt{2}}{1 - \sqrt{2}}})(\frac{1+\sqrt{2}}{1+\sqrt{2}})$

⇒ $(\frac{(3 - \sqrt{5} - 2\sqrt{2})(1+\sqrt{2}) }{(1 - \sqrt{2})(1 +\sqrt{2})}})$

⇒ $(\frac{3 - \sqrt{5} - 2\sqrt{2} + 3\sqrt{2} - \sqrt{10} - 4 }{(1)^2 - (\sqrt{2})^2}})$

⇒ $(\frac{-1 - \sqrt{5} +\sqrt{2} - \sqrt{10}}{ -1}})$

⇒ $1 + \sqrt{5} -\sqrt{2} + \sqrt{10}$

∴ The denominator is rationalised to -1