Question

2 root 3 - root 5 by 2 root 2 + 3 root 3
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Answer 1

Answer:

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

now we need to rationalize the denominator

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

or

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

or

$\frac{(4 \sqrt{6} - 18 ) - (2 \sqrt{10} - 3 \sqrt{15} )}{8 - 27}$

or

$\frac{4 \sqrt{6} - 18 - 2 \sqrt{10} + 3 \sqrt{15} }{ - 19}$

or

$\frac{18 + 2 \sqrt{10} - 4 \sqrt{6} - 3 \sqrt{15} }{19}$

and this is the final answer

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