Question

Simplify
2√30/√6-3√140/√28+√55/√99

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{2 \sqrt{30} }{ \sqrt{6} } - \frac{3 \sqrt{140} }{ \sqrt{28} } + \frac{ \sqrt{55} }{ \sqrt{99} } \\ \\ (by \: splitting \: we \: get) \\ \\ = \frac{2 \sqrt{30} }{ \sqrt{6} } - \frac{3 \sqrt{2 \times 2 \times 7 \times 5} }{ \sqrt{2 \times 2 \times 7} } + \frac{ \sqrt{55} }{ \sqrt{3 \times 3 \times 11} } \\ \\ = \frac{2 \sqrt{30} }{ \sqrt{6} } - \frac{3 \times 2 \sqrt{35} }{2 \sqrt{7} } + \frac{ \sqrt{55} }{3 \sqrt{11} } \\ \\ on \: rationalizing \: we \: get \\ \\ \frac{2 \sqrt{30} }{ \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} } - \frac{6 \sqrt{35} }{2 \sqrt{7} } \times \frac{2 \sqrt{7} }{2 \sqrt{7} } + \frac{ \sqrt{55} }{3 \sqrt{11} } \times \frac{3 \sqrt{11} }{3 \sqrt{11} } \\ \\ = \frac{2 \sqrt{30} \times \sqrt{6} }{ \sqrt{6} \times \sqrt{6} } - \frac{6 \times 2 \sqrt{35} \times \sqrt{7} }{2 \sqrt{7} \times 2 \sqrt{7} } + \frac{ \sqrt{55} \times 3 \sqrt{11} }{3 \sqrt{11} \times 3 \sqrt{11} } \\ \\ (splitting \: again) \\ \\ = \frac{2 \sqrt{6 \times 6 \times 5} }{6} - \frac{12 \sqrt{7 \times 7 \times 5} }{28} + \frac{3 \sqrt{11 \times 11 \times 5} }{99} \\ \\ = \frac{2 \times 6 \sqrt{5} }{6} - \frac{12 \times 7 \sqrt{5} }{28} + \frac{3 \times 11 \sqrt{5} }{99} \\ \\ (cancelling) \\ \\ = 2 \sqrt{5} - 3 \sqrt{5} + \frac{ \sqrt{5} }{3} \\ \\ (or \: we \: can \: write) \\ \\ = \frac{2 \sqrt{5} \times 3 - 3 \sqrt{5} \times 3 + \sqrt{5} \times 1}{3} \\ \\ = \frac{6 \sqrt{5} - 9 \sqrt{5} + \sqrt{5} }{3}$


Hope this helps!!!

@Mahak24

Thanks...
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