Simplify \(\sqrt{8}\) to \(2\sqrt{2}\).
\[2\sqrt{2}+\sqrt{\frac{9}{2}}-\frac{1}{\sqrt{2}}+3\sqrt{{(-2)}^{2}}\]
Simplify \(\sqrt{\frac{9}{2}}\) to \(\frac{\sqrt{9}}{\sqrt{2}}\).
\[2\sqrt{2}+\frac{\sqrt{9}}{\sqrt{2}}-\frac{1}{\sqrt{2}}+3\sqrt{{(-2)}^{2}}\]
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[2\sqrt{2}+\frac{3}{\sqrt{2}}-\frac{1}{\sqrt{2}}+3\sqrt{{(-2)}^{2}}\]
Since the power of 2 is even, the result will be positive.
\[2\sqrt{2}+\frac{3}{\sqrt{2}}-\frac{1}{\sqrt{2}}+3\sqrt{{2}^{2}}\]
Simplify \(\sqrt{{2}^{2}}\) to \(2\).
\[2\sqrt{2}+\frac{3}{\sqrt{2}}-\frac{1}{\sqrt{2}}+3\times 2\]
Rationalize the denominator: \(\frac{3}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{3\sqrt{2}}{2}\).
\[2\sqrt{2}+\frac{3\sqrt{2}}{2}-\frac{1}{\sqrt{2}}+3\times 2\]
Rationalize the denominator: \(\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}\).
\[2\sqrt{2}+\frac{3\sqrt{2}}{2}-\frac{\sqrt{2}}{2}+3\times 2\]
Simplify \(3\times 2\) to \(6\).
\[2\sqrt{2}+\frac{3\sqrt{2}}{2}-\frac{\sqrt{2}}{2}+6\]
Collect like terms.
\[(2\sqrt{2}+\frac{3\sqrt{2}}{2}-\frac{\sqrt{2}}{2})+6\]
Simplify.
\[\frac{6\sqrt{2}}{2}+6\]
Decimal Form: 10.242641
(6*sqrt(2))/2+6
