Question

Solve this please .....​

Answer 1

$\frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } = \frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } \times \frac{ \sqrt{10 } - \sqrt{3} }{ \sqrt{10} - \sqrt{3} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{7 \sqrt{30} - 21}{10 - 3} = \sqrt{30} - 3$

now

$\frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } = \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } \times \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6} - \sqrt{5} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2 \sqrt{30} - 10}{6 - 5} = 2 \sqrt{30} - 10$

and

$\frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } = \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } \times \frac{ \sqrt{15} - 3 \sqrt{2} }{ \sqrt{15} - 3 \sqrt{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3 \sqrt{30 }- 18 }{15 - 18} = 6 - \sqrt{30}$

finally

$\frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } - \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } = (\sqrt{30} - 3) - (2 \sqrt{30} - 10) - (6 - \sqrt{30} ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \sqrt{30} - 2 \sqrt{30} + 10 - 9 = 1$

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the answer to your question is 1

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Answer 2

Answer:

fristly we rationalize

ans is in this attachment..

13 is the ans of this question