Question

7 root 3/ root 10 + root 3 - 2 root 5/ root 6+ root 5 - 3 Root 2 /root 15 + 3 Root 2ANSWER PLEASE.

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } - \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3 }$

On rationalizing the denominator we get,

$= \frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } \times \frac{ \sqrt{10} - \sqrt{3} }{ \sqrt{10} - \sqrt{3} } - \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } \times \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6} - \sqrt{5} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3} \times \frac{ \sqrt{15} - 3 }{ \sqrt{15} - 3} \\ \\ = \frac{7 \sqrt{3}( \sqrt{10} - \sqrt{3} )}{ {( \sqrt{10} )}^{2} - {( \sqrt{3} )}^{2} } - \frac{2 \sqrt{5} ( \sqrt{6} - \sqrt{5}) }{ {( \sqrt{6}) }^{2} - {( \sqrt{5}) }^{2} } - \frac{3 \sqrt{2}( \sqrt{15} - 3) }{ {( \sqrt{15}) }^{2} - {(3)}^{2} } \\ \\ = \frac{7 \sqrt{30} - 21}{10 - 3} - \frac{2 \sqrt{30} - 10}{6 - 5} - \frac{3 \sqrt{30} - 9 \sqrt{2} }{15 - 9} \\ \\ = \sqrt{30} - 3 - 2 \sqrt{30} + 10 - \frac{ \sqrt{30} - 3 \sqrt{2} }{2} \\ \\ = - \sqrt{30} + 7 - \frac{ \sqrt{30} - 3 \sqrt{2} }{2} \\ \\ = \frac{ - \sqrt{30} \times 2 + 7 \times 2 - \sqrt{30} + 3 \sqrt{2} }{2} \\ \\ = \frac{ - 2 \sqrt{30} + 14 - \sqrt{30} + 3 \sqrt{2} }{2} \\ \\ = \frac{14 + 3 \sqrt{2} - 3 \sqrt{30} }{2}$

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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