Answer: The correct option is
(D) [tex]20x^{50}.[/tex]
Step-by-step explanation: We are given to find the simplified form of the following radical expression :
[tex]E=\sqrt{400x^{100}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following properties :
[tex](i)~(ab)^c=a^cb^c,\\\\(ii)~\sqrt{a^b}=a^{\frac{b}{2}}.[/tex]
From expression (i), we get
[tex]E\\\\=\sqrt{400x^{100}}\\\\=\sqrt{(20x^{50})^2}\\\\=(20x^{50})^\frac{2}{2}\\\\=20x^{50}.[/tex]
Thus, the required simplified form of the given expression is [tex]20x^{50}.[/tex]
Option (D) is CORRECT.
