Since the power of 2 is even, the result will be positive.
\[G=\frac{\sqrt{{6}^{2}}-\sqrt{32}}{2+\sqrt{7}\sqrt{35}-\sqrt{245}}\]
Simplify \(\sqrt{{6}^{2}}\) to \(6\).
\[G=\frac{6-\sqrt{32}}{2+\sqrt{7}\sqrt{35}-\sqrt{245}}\]
Simplify \(\sqrt{32}\) to \(4\sqrt{2}\).
\[G=\frac{6-4\sqrt{2}}{2+\sqrt{7}\sqrt{35}-\sqrt{245}}\]
Factor out the common term \(2\).
\[G=\frac{2(3-2\sqrt{2})}{2+\sqrt{7}\sqrt{35}-\sqrt{245}}\]
Simplify \(\sqrt{245}\) to \(7\sqrt{5}\).
\[G=\frac{2(3-2\sqrt{2})}{2+\sqrt{7}\sqrt{35}-7\sqrt{5}}\]
Simplify \(\sqrt{7}\sqrt{35}\) to \(\sqrt{245}\).
\[G=\frac{2(3-2\sqrt{2})}{2+\sqrt{245}-7\sqrt{5}}\]
Simplify \(\sqrt{245}\) to \(7\sqrt{5}\).
\[G=\frac{2(3-2\sqrt{2})}{2+7\sqrt{5}-7\sqrt{5}}\]
Simplify \(2+7\sqrt{5}-7\sqrt{5}\) to \(2\).
\[G=\frac{2(3-2\sqrt{2})}{2}\]
Cancel \(2\).
\[G=3-2\sqrt{2}\]
Decimal Form: 0.171573
G=3-2*sqrt(2)
