Question

Need help with simplifying roots (medal and fan)

Answer 1

\[(-\frac{ \sqrt{2} }{ 2 } \times \frac{ 1 }{ 2 }) - (\frac{ \sqrt{2} }{ 2} \times \frac{ \sqrt{3} }{ 2 })\]

Answer 2

The answer is:
\[-\frac{ 1 }{ 4 }(\sqrt{2}+\sqrt{6})\]

Answer 3

I don't understand how this is the answer. I must be doing something very wrong. Here's my work:
\[\frac{- \sqrt{2} }{ 4 }-\frac{ \sqrt{6} }{ 4 }\]
Then:
\[\frac{ -\sqrt{2} -\sqrt{6}}{ 4 }\]

Answer 4

\(\bf \left(-\cfrac{ \sqrt{2} }{ 2 } \times \cfrac{ 1 }{ 2 }\right) -\left( \cfrac{ \sqrt{2} }{ 2} \times \cfrac{ \sqrt{3} }{ 2 } \right)\implies \cfrac{ -\sqrt{2} -\sqrt{6}}{ 4 }
\\ \quad \\
\cfrac{-\sqrt{2}}{4}+\cfrac{-\sqrt{6}}{4}\implies \left( -\cfrac{1}{4}\sqrt{2} \right)+\left( -\cfrac{1}{4}\sqrt{6} \right)\impliedby \textit{common factor}
\\ \quad \\
-\cfrac{1}{4}\left( \sqrt{2}+\sqrt{6} \right)\)