Question

1/√2 + 2/√8 +3/√18+4/√32=

Answer 1

$\frac{1}{ \sqrt{2} } + \frac{2}{ \sqrt{8} } + \frac{3}{ \sqrt{18} } + \frac{4}{ \sqrt{32} } = \\ \frac{ \sqrt{2} }{2} + \frac{2}{2 \sqrt{2} } + \frac{3}{3 \sqrt{2} } + \frac{4}{4 \sqrt{2} } = \\ \frac{ \sqrt{2} }{2} + \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{2} } = \\ \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2} = \\ \frac{4 \sqrt{2} }{2} = 2 \sqrt{2}$

Answer 2

$\it \frac{1}{ \sqrt{2} } + \frac{2}{ \sqrt{8} } + \frac{3}{ \sqrt{18} } + \frac{4}{ \sqrt{32} } = \\ \\ \it ^{ \sqrt{2} )} \frac{1}{ \sqrt{2} } \: + \: ^{ \sqrt{2} )} \frac{2}{2 \sqrt{2} } \: + \: ^{ \sqrt{2}) } \frac{3}{3 \sqrt{2} } \: + \: ^{ \sqrt{2}) } \frac{4}{4 \sqrt{2} } = \\ \\ \it \frac{ \sqrt{2} }{2} + \frac{2 \sqrt{2} }{2 \cdot 2} + \frac{3 \sqrt{2} }{3 \cdot 2} + \frac{4 \sqrt{2} }{4 \cdot 2} = \\ \\ \it \frac{ \sqrt{2} }{2} + \frac{2 \sqrt{2} }{4} + \frac{3 \sqrt{2} }{6} + \frac{4 \sqrt{2} }{8} = \\ \\ \it \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2} = \frac{4 \sqrt{2} }{2} = \mathbf{2 \sqrt{2} }$