Question

Simplify: 7√3 3√2 2√5
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√10+√3 √15+3√2 √6+√5

Answer 1

Identity used :

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


$\frac{7 \sqrt{3} }{ \sqrt{10} - \sqrt{3} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } - \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } \\ \\ \bf \: on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{7 \sqrt{3} }{ \sqrt{10} - \sqrt{3} } \times \frac{ \sqrt{10} + \sqrt{3} }{ \sqrt{10} + \sqrt{3} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } \times \frac{ \sqrt{15} - 3 \sqrt{2} }{ \sqrt{15} - 3 \sqrt{2} } - \frac{ 2\sqrt{5} }{ \sqrt{6} + \sqrt{5} } \times \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6} - \sqrt{5} } \\ \\ = \frac{7 \sqrt{30} + 7 {( \sqrt{3}) }^{2} }{ {( \sqrt{10} )}^{2} - {( \sqrt{3}) }^{2} } - \frac{3 \sqrt{30} - {(3 \sqrt{2} )}^{2} }{ {( \sqrt{15} )}^{2} - {(3 \sqrt{2}) }^{2} } - \frac{2 \sqrt{30} - 2( { \sqrt{5} )}^{2} }{ {( \sqrt{6}) }^{2} - {( \sqrt{5}) }^{2} } \\ \\ = \frac{7 \sqrt{30} - 7(3) }{10 - 3} - \frac{3 \sqrt{30} - 18}{15 - 18} - \frac{2 \sqrt{30} - 2(5) }{6 - 5} \\ \\ = \frac{7( \sqrt{30} - 3)}{7} - \frac{3( \sqrt{30} - 6)}{ - 3} - (2 \sqrt{30} - 10) \\ \\ = ( \sqrt{30} - 3) - ( - \sqrt{30} + 6) - (2 \sqrt{30} - 10) \\ \\ = \sqrt{30} - 3 + \sqrt{30} + 6 - 2 \sqrt{30} + 10 \\ \\ = 2 \sqrt{30} - 2 \sqrt{30} + 16 - 3 \\ \\ = 13$

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Answer 2

Answer:

hey mate, refer to the following pic for explanation:

hope you are satisfied with the answer

thank you for the question