Question

Rationalise 4 upon 3 + root 5 - 2 root 2​

Answer 1

$\small \bf \pink{hey \: mate \: here \: is \: ur \: ans} \\ \\ \small \bf \pink{ \huge \: solution} \\ \\ \small \bf \pink{ \frac{4}{3 + \sqrt{5} - 2 \sqrt{2} } } \\ \\ \small \bf \pink{ \frac{4(3 + \sqrt{5} + 2 \sqrt{2}) }{(3 + \sqrt{5} - 2 \sqrt{2})(3 + \sqrt{5} + 2 \sqrt{2}) } } \\ \\ \small \bf \pink{using \: to \: this \: identity} \\ \\ \small \bf \pink{ {a}^{2} - {b}^{2} = (a + b)(a - b)} \\ \\ \small \bf \pink{ \frac{4(3 + \sqrt{5} + 2 \sqrt{2}) }{(3 + \sqrt{5} )^{2} - (2 \sqrt{2})^{2} } } \\ \\ \small \bf \pink{ \frac{4(3 + \sqrt{5} + 2 \sqrt{2} )}{ {3}^{2} + 2 \times 3 \times \sqrt{5} + { \sqrt{5} }^{2} - 8 } } \\ \\ \small \bf \pink{ \frac{4(3 + \sqrt{5} + 2 \sqrt{2} )}{9 + 5 + 6 \sqrt{5} - 8} } \\ \\ \small \bf \pink{ \frac{4(3 + \sqrt{5} + 2 \sqrt{2}) }{14 - 8 + 6 \sqrt{5} } } \\ \\ \small \bf \pink{ \frac{4(3 + \sqrt{5} + 2 \sqrt{2}) }{6 + 6 \sqrt{5} } } \\ \\ \small \bf \pink{ \frac{4(3 + \sqrt{5} + 2 \sqrt{2}) }{6(1 + \sqrt{5}) } } \\ \\ \small \bf \pink{ \frac{2(3 + \sqrt{5} + 2 \sqrt{2}) }{3(1 + \sqrt{5}) } \: \: ans}$