Question

rationalise the denominator of 1/3√3+2√2

Answer 1

$\textbf{ \underline{ \huge{ Hello Mate! }}}$

$\frac{1}{3 \sqrt{3} + 2 \sqrt{2} } \\ rationalize \\ \frac{1}{3 \sqrt{3} + 2 \sqrt{2} } \times \frac{3 \sqrt{3} - 2 \sqrt{2} }{3 \sqrt{3} - 2 \sqrt{2} } \\ = \frac{3 \sqrt{3} - 2 \sqrt{2} }{ {(3 \sqrt{3} )}^{2} - {(2 \sqrt{2} )}^{2} } \\ = \frac{3 \sqrt{3} - 2 \sqrt{2} }{9 \times 3 - 4 \times 2} \\ = \frac{3 \sqrt{3} - 2 \sqrt{2} }{27 - 8} = \frac{3 \sqrt{3} - 2 \sqrt{2} }{19}$
Have great future ahead!

Answer 2

$\bf \large \it \: Hey \: User!!!$

$given \: = > \frac{1}{3 \sqrt{3} + 2 \sqrt{2} } \\ \\ = \frac{1}{3 \sqrt{3} + 2 \sqrt{2} } \times \frac{3 \sqrt{3} - 2 \sqrt{2} }{3 \sqrt{3} - 2 \sqrt{ 2} } \\ \\ = \frac{3 \sqrt{3} - 2 \sqrt{2} }{(3 \sqrt{ 3 } + 2 \sqrt{2})(3 \sqrt{3} - 2 \sqrt{2} ) } \\ \\ = \frac{3 \sqrt{3} - 2 \sqrt{2} }{ {(3 \sqrt{3} )}^{2} - {(2 \sqrt{2}) }^{2} } \\ \\ = \frac{3 \sqrt{3} - 2 \sqrt{2} }{27 - 8} \\ \\ = \boxed{\frac{3 \sqrt{3} - 2 \sqrt{2} }{19} } \: final \: answer$

$\bf \large \it{Cheers!!!}$