(5 raised to 2 square root of 20)(2 raised to 2 square root of 4)
You asked:
Evaluate the expression: \({5}^{2} \cdot \sqrt{20} \cdot {2}^{2} \cdot \sqrt{4}\)
MathBot Answer:
\[{5}^{2} \cdot \sqrt{20} \cdot {2}^{2} \cdot \sqrt{4} = 400 \sqrt{5} \approx 894.42719099991587856366946749251049\]
\[\begin{aligned}{5}^{2} \cdot \sqrt{20} \cdot {2}^{2} \cdot \sqrt{4}& = 5^{2} \cdot \sqrt{20} \cdot 2^{2} \cdot \sqrt{4}\\& = 25 \cdot \sqrt{20} \cdot 2^{2} \cdot \sqrt{4}\\& = 25 \cdot 2 \cdot \sqrt{5} \cdot 2^{2} \cdot \sqrt{4}\\& = 25 \cdot 2 \cdot \sqrt{5} \cdot 4 \cdot \sqrt{4}\\& = 25 \cdot 2 \cdot \sqrt{5} \cdot 4 \cdot 2\\& = 50 \cdot \sqrt{5} \cdot 4 \cdot 2\\& = 200 \cdot \sqrt{5} \cdot 2\\& = 400 \cdot \sqrt{5}\end{aligned}\]