\frac{4^{\frac{1}{2}}\cdot \left(5.64\right)^{\frac{1}{2}}}{5^{\frac{1}{2}}}
You asked:
Evaluate the expression: \(\frac{{4}^{\frac{1}{2}} \cdot {5.64}^{\frac{1}{2}}}{{5}^{\frac{1}{2}}}\)
MathBot Answer:
\[\frac{{4}^{\frac{1}{2}} \cdot {5.64}^{\frac{1}{2}}}{{5}^{\frac{1}{2}}} = \frac{2 \sqrt{705}}{25} \approx 2.12414688757628058719742875409242\]
\[\begin{aligned}\frac{{4}^{\frac{1}{2}} \cdot {5.64}^{\frac{1}{2}}}{{5}^{\frac{1}{2}}}& = \sqrt{4} \cdot \sqrt{5 + \frac{64}{100}} \cdot \frac{1}{\sqrt{5}}\\& = 2 \cdot \sqrt{5 + \frac{64}{100}} \cdot \frac{1}{\sqrt{5}}\\& = 2 \cdot \sqrt{5 + \frac{16}{25}} \cdot \frac{1}{\sqrt{5}}\\& = 2 \cdot \sqrt{\frac{141}{25}} \cdot \frac{1}{\sqrt{5}}\\& = 2 \cdot \frac{1}{5} \cdot \sqrt{141} \cdot \frac{1}{\sqrt{5}}\\& = 2 \cdot \frac{1}{25} \cdot \sqrt{705}\\& = \frac{2}{25} \cdot \sqrt{705}\end{aligned}\]