## anonymous one year ago Need help with simplifying roots (medal and fan)

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1. anonymous

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

2. anonymous

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

3. anonymous

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: $\frac{ -\sqrt{2} -\sqrt{6}}{ 4 }$

4. anonymous

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