Simplify \({3.5}^{2}\) to \(12.25\).
\[\sqrt{12.25+{(\frac{9}{2})}^{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\sqrt{12.25+\frac{{9}^{2}}{{2}^{2}}}\]
Simplify \({9}^{2}\) to \(81\).
\[\sqrt{12.25+\frac{81}{{2}^{2}}}\]
Simplify \({2}^{2}\) to \(4\).
\[\sqrt{12.25+\frac{81}{4}}\]
Simplify \(12.25+\frac{81}{4}\) to \(\frac{65}{2}\).
\[\sqrt{\frac{65}{2}}\]
Simplify.
\[\frac{\sqrt{65}}{\sqrt{2}}\]
Rationalize the denominator: \(\frac{\sqrt{65}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{65}\sqrt{2}}{2}\).
\[\frac{\sqrt{65}\sqrt{2}}{2}\]
Simplify \(\sqrt{65}\sqrt{2}\) to \(\sqrt{130}\).
\[\frac{\sqrt{130}}{2}\]
Decimal Form: 5.700877
sqrt(130)/2
