Question

2 root 30 minus 3 root 15 upon root 6 + root 5 please rationalize it​

Answer 1

$\frak{ \frac{2 \sqrt{30} - 3 \sqrt{15} }{ \sqrt{6} + \sqrt{5} } } \\ \\ = > \frak{ \frac{2 \sqrt{30} - 3 \sqrt{15} }{ \sqrt{6} + \sqrt{5} } } \times {\huge{(}} \frac{ \sqrt{6 } - \sqrt{5} }{ \sqrt{6} - \sqrt{5} } \huge{)} \\ \\ = > \frac{2 \sqrt{180} - 2 \sqrt{150} - 3 \sqrt{90} + 3 \sqrt{75} }{ {( \sqrt{6} )}^{2} - {( \sqrt{5} )}^{2} } \\ \\ = > \frac{12 \sqrt{5} - 10 \sqrt{6} - 9 \sqrt{10} + 15 \sqrt{3} }{6 - 5} \\ \\ = > \red{12 \sqrt{5} - 9 \sqrt{10} - 10 \sqrt{6} + 15 \sqrt{3} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf{ \huge{Or,} } \\ = > \red{3 \sqrt{5} (4 - 3 \sqrt{2} ) - 5 \sqrt{3} (2 \sqrt{2} + 3)}$

#BAL