Given the expression:
[tex]\sqrt{4x^2}\cdot\sqrt{20x^2}[/tex]You can simplify each Radical as follows, in order to find an equivalent expression:
1. If you decompose the coefficient 4 and the coefficient 20 into their Prime Factors, you get:
[tex]\begin{gathered} 4=2\cdot2=2^2 \\ \\ 20=2\cdot2\cdot5=2^2\cdot5 \end{gathered}[/tex]Rewrite the Radicands:
[tex]=\sqrt{2^2x^2}\cdot\sqrt{2^25^2x^2}[/tex]2. Apply this Property for Radicals:
[tex]\sqrt[n]{b^n}=b[/tex]Then, you get:
[tex]\begin{gathered} =2x\cdot2x\cdot\sqrt{5} \\ \\ =4x^2\sqrt{5} \end{gathered}[/tex]Hence, the answer is: Option A.