Question

4√2/√15-3√2+3√5/√10-√3+5√3/√6+√5

Answer 1

Heya !!!

$\frac{4 \sqrt{2} }{ \sqrt{15} - 3 \sqrt{2} } + \frac{3 \sqrt{5} }{ \sqrt{10} - \sqrt{3} } + \frac{5 \sqrt{3} }{ \sqrt{6} + \sqrt{5} }$

On rationalizing the denominator we get,

$= \frac{4 \sqrt{2} }{ \sqrt{15} - 3 \sqrt{2} } \times \frac{ \sqrt{15} + 3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } + \frac{3 \sqrt{5} }{ \sqrt{10} - \sqrt{3} } \times \frac{ \sqrt{10} + \sqrt{3} }{ \sqrt{10} + \sqrt{3} } + \frac{5 \sqrt{3} }{ \sqrt{6} + \sqrt{5} } \times \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6} - \sqrt{5} } \\ \\ = \frac{4 \sqrt{2} ( \sqrt{15} + 3 \sqrt{2} )}{ {( \sqrt{15}) }^{2} - {(3 \sqrt{2} )}^{2} } + \frac{3 \sqrt{5}( \sqrt{10} + \sqrt{3} )}{ {( \sqrt{10}) }^{2} - {( \sqrt{3} )}^{2} } + \frac{5 \sqrt{3} ( \sqrt{6} - \sqrt{5}) }{ {( \sqrt{6}) }^{2} - {( \sqrt{5}) }^{2} } \\ \\ = \frac{4 \sqrt{30} + 24 }{15 - 18} + \frac{3 \sqrt{50} + 3 \sqrt{15} }{10 - 3} + \frac{5 \sqrt{18} - 5 \sqrt{15} }{6 - 5} \\ \\ = \frac{4 \sqrt{30} + 24}{ - 3} + \frac{3 \sqrt{2 \times 5 \times 5} + 3 \sqrt{15} }{7} + 5 \sqrt{3 \times 3 \times 2} - 5 \sqrt{15} \\ \\ = \frac{ - 4 \sqrt{30} - 24}{3} + \frac{15 \sqrt{2} + 3 \sqrt{15} }{7} + 15 \sqrt{2} - 5 \sqrt{15} \\ \\ = \frac{ - 4 \sqrt{30} \times 7 - 24 \times 7 + 15 \sqrt{2} \times 3 + 3 \sqrt{15} \times 3 + 15 \sqrt{2} \times 21 - 5 \sqrt{15} \times 21}{21} \\ \\ = \frac{ - 28 \sqrt{30} - 168 + 45 \sqrt{2} + 9 \sqrt{15} + 315 \sqrt{2} - 105 \sqrt{15} }{21} \\ \\ = \frac{ - 28 \sqrt{30} - 168 + 360 \sqrt{2} - 96 \sqrt{15} }{21}$


Hope this helps ☺

Answer 2

Answer:

this is your right answer