Factor out the common term \(3\).
\[\sqrt{{(3(1-\sqrt{3}))}^{2}+{(-3-3\sqrt{3})}^{2}}\]
Factor out the common term \(3\).
\[\sqrt{{(3(1-\sqrt{3}))}^{2}+{(-3(1+\sqrt{3}))}^{2}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\sqrt{{3}^{2}{(1-\sqrt{3})}^{2}+{(-3(1+\sqrt{3}))}^{2}}\]
Simplify \({3}^{2}\) to \(9\).
\[\sqrt{9{(1-\sqrt{3})}^{2}+{(-3(1+\sqrt{3}))}^{2}}\]
Since the power of 2 is even, the result will be positive.
\[\sqrt{9{(1-\sqrt{3})}^{2}+{(3(1+\sqrt{3}))}^{2}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\sqrt{9{(1-\sqrt{3})}^{2}+{3}^{2}{(1+\sqrt{3})}^{2}}\]
Simplify \({3}^{2}\) to \(9\).
\[\sqrt{9{(1-\sqrt{3})}^{2}+9{(1+\sqrt{3})}^{2}}\]
Factor out the common term \(9\).
\[\sqrt{9({(1-\sqrt{3})}^{2}+{(1+\sqrt{3})}^{2})}\]
Expand.
\[\sqrt{9(1-2\sqrt{3}+{\sqrt{3}}^{2}+1+2\sqrt{3}+{\sqrt{3}}^{2})}\]
Use this rule: \({\sqrt{x}}^{2}=x\).
\[\sqrt{9(1-2\sqrt{3}+3+1+2\sqrt{3}+3)}\]
Collect like terms.
\[\sqrt{9((1+3+1+3)+(-2\sqrt{3}+2\sqrt{3}))}\]
Simplify \((1+3+1+3)+(-2\sqrt{3}+2\sqrt{3})\) to \(8\).
\[\sqrt{9\times 8}\]
Simplify \(9\times 8\) to \(72\).
\[\sqrt{72}\]
Simplify \(\sqrt{72}\) to \(6\sqrt{2}\).
\[6\sqrt{2}\]
Decimal Form: 8.485281
6*sqrt(2)
