Question

one upon root 3 + root 2 minus 2 upon root 5 minus root 3 minus 3 upon root 2 minus root 5

Answer 1

Hey friend,
Here is the answer you were looking for :


Identity used :

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

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

On rationalizing the denominators we get,

$= \frac{1}{ \sqrt{3} + \sqrt{2} } \times \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } - \frac{2}{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } - \frac{3}{ \sqrt{2} - \sqrt{5} } \times \frac{ \sqrt{2} + \sqrt{5} }{ \sqrt{2} + \sqrt{5} } \\ \\ = \frac{ \sqrt{3} - \sqrt{2} }{ {( \sqrt{3} )}^{2} - {( \sqrt{2} )}^{2} } - \frac{2( \sqrt{5} + \sqrt{3} )}{ {( \sqrt{5} )}^{2} - {( \sqrt{3}) }^{2} } - \frac{3( \sqrt{2} + \sqrt{5} ) }{ {( \sqrt{2} )}^{2} - {( \sqrt{5} )}^{2} } \\ \\ = \frac{ \sqrt{3} - \sqrt{2} }{3 - 2} - \frac{2 \sqrt{5} + 2 \sqrt{3} }{5 - 3} - \frac{3 \sqrt{2} + 3 \sqrt{5} }{2 - 5} \\ \\ = \sqrt{3} - \sqrt{2} - \frac{2 \sqrt{5} + 2 \sqrt{3} }{2} - \frac{3 \sqrt{2} + 3 \sqrt{5} }{ - 3} \\ \\ = \sqrt{3} - \sqrt{2} - \sqrt{5} - \sqrt{3} + \sqrt{2} + \sqrt{5} \\ \\ = 0$


Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
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Answer 2

Answer:

Step-by-step explanation: