Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\sqrt{\frac{{3}^{2}}{{2}^{2}}-4\times \frac{-1}{2}}\]
Simplify \({3}^{2}\) to \(9\).
\[\sqrt{\frac{9}{{2}^{2}}-4\times \frac{-1}{2}}\]
Simplify \({2}^{2}\) to \(4\).
\[\sqrt{\frac{9}{4}-4\times \frac{-1}{2}}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\sqrt{\frac{9}{4}-\frac{-4}{2}}\]
Move the negative sign to the left.
\[\sqrt{\frac{9}{4}-(-\frac{4}{2})}\]
Simplify \(\frac{4}{2}\) to \(2\).
\[\sqrt{\frac{9}{4}-(-2)}\]
Remove parentheses.
\[\sqrt{\frac{9}{4}+2}\]
Simplify \(\frac{9}{4}+2\) to \(\frac{17}{4}\).
\[\sqrt{\frac{17}{4}}\]
Simplify.
\[\frac{\sqrt{17}}{\sqrt{4}}\]
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[\frac{\sqrt{17}}{2}\]
Decimal Form: 2.061553
sqrt(17)/2
