Question

hey!!!!

please solve question no. 8

Thanx!!!

Answer 1

Hey friend,
Here is the answer you were looking for:
$1) \\ 3 \sqrt{45} - \sqrt{125} + \sqrt{200} - \sqrt{50} \\ \\ = 3 \sqrt{ 3 \times 3 \times 5} - \sqrt{5 \times 5 \times 5} + \sqrt{2 \times 2 \times 2 \times 5 \times 5} - \sqrt{5 \times 5 \times 2} \\ \\ = 3 \times 3 \sqrt{5} - 5 \sqrt{5} + 2 \times 5 \sqrt{2} - 5 \sqrt{2} \\ \\ = 9 \sqrt{5} - 5 \sqrt{5} + 10 \sqrt{2} - 5 \sqrt{2} \\ \\ = 4 \sqrt{5} + 5 \sqrt{2} \\ \\ = 5 \sqrt{2} + 4 \sqrt{5} \\ \\ 2) \\ \frac{2 \sqrt{30} }{ \sqrt{6} } - \frac{3 \sqrt{140} }{ \sqrt{28} } + \frac{ \sqrt{55} }{ \sqrt{99} } \\ \\ = \frac{2 \sqrt{30} }{ \sqrt{6} } - \frac{3 \sqrt{2 \times 2 \times 5 \times 7} }{ \sqrt{2 \times 2 \times 7} } + \frac{ \sqrt{55} }{ \sqrt{3 \times 3 \times 11} } \\ \\ = \frac{2 \sqrt{30} }{ \sqrt{6} } - \frac{3 \times 2 \sqrt{35} }{2 \sqrt{7} } + \frac{ \sqrt{55} }{3 \sqrt{11} } \\ \\ = \frac{2 \sqrt{30} }{ \sqrt{6} } - \frac{6 \sqrt{35} }{2 \sqrt{7} } + \frac{ \sqrt{55} }{3 \sqrt{11} } \\ \\ = \frac{2 \sqrt{30} }{ \sqrt{6} } - \frac{3 \sqrt{35} }{ \sqrt{7} } + \frac{ \sqrt{55} }{3 \sqrt{11} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{2 \sqrt{30} }{ \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} } - \frac{3 \sqrt{35} }{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } + \frac{ \sqrt{55} }{3 \sqrt{11} } \times \frac{ 3\sqrt{11} }{3 \sqrt{11} } \\ \\ = \frac{2 \sqrt{30} \times \sqrt{6} }{ \sqrt{6} \times \sqrt{6} } - \frac{3 \sqrt{35} \times \sqrt{7} }{ \sqrt{7} \times \sqrt{7} } + \frac{ \sqrt{55} \times 3 \sqrt{11} }{3 \sqrt{11} \times 3 \sqrt{11} } \\ \\ = \frac{2 \sqrt{180} }{6} - \frac{3 \sqrt{245} }{7} + \frac{3 \sqrt{605} }{99} \\ \\ = \frac{2 \sqrt{3 \times 2 \times 5 \times 2 \times 3} }{6} - \frac{3 \sqrt{5 \times 7 \times 7} }{7} + \frac{3 \sqrt{5 \times 11 \times 11} }{99} \\ \\ = \frac{2 \times 2 \times 3 \sqrt{5} }{6} - \frac{3 \times 7 \sqrt{5} }{7} + \frac{3 \times 11 \sqrt{5} }{99} \\ \\ = \frac{12 \sqrt{5} }{6} - \frac{21 \sqrt{5} }{7} + \frac{33 \sqrt{5} }{99} \\ \\ = 2 \sqrt{5} - 3 \sqrt{5} + \frac{ \sqrt{5} }{3} \\ \\ 3) \\ \sqrt{72} + \sqrt{800} - \sqrt{18} \\ \\ = \sqrt{2 \times 2 \times 3 \times 3 \times 2} + \sqrt{2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 2} - \sqrt{3 \times 3 \times 2} \\ \\ = 2 \times 3 \sqrt{2} + 2 \times 2 \times 5 \sqrt{2} - 3\sqrt{2} \\ \\ = 6 \sqrt{2} + 20 \sqrt{2} - 3 \sqrt{2} \\ \\ = 26 \sqrt{2} - 3 \sqrt{2} \\ \\ = 23 \sqrt{2}$


Hope this helps!!!

@Mahak24

Thanks....
☺☺