Question

simplify 4√2/√15-3√2 + 3√5/√10-√3 + 5√5/√6+√5​

Answer 1

Answer:

Please refer below first

Step-by-step explanation:

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

$rationalizing \: denominator \: get$

$\frac{4 \sqrt{2} }{15 - 3 \sqrt{2} } \: \times \frac{ \sqrt{15 } - 3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} }$

$\frac{3 \sqrt{5} }{ \sqrt{10} - \sqrt{3} }$

$= \frac{4 \sqrt{2}( \sqrt{15} + 3 \sqrt{2} ) }{ \sqrt{15 {}^{2} } - ( \sqrt{2 {}^{2} } }$