Answer: The simplified form of the radical is [tex]20x^{50}.[/tex]
Step-by-step explanation: We are given to find the simplified form of the following radical:
[tex]R=\sqrt{400x^{100}}.[/tex]
We will be using the following square root property:
[tex]\sqrt{a}=a^{\frac{1}{2}}.[/tex]
The simplification is as follows:
[tex]R\\\\=\sqrt{400x^{100}}\\\\=(400x^{100})^\frac{1}{2}\\\\=(20^2x^{100})^\frac{1}{2}\\\\=20^{2\times\frac{1}{2}}\times x^{100\times\frac{1}{2}}\\\\=20\times x^{50}\\\\=20x^{50}.[/tex]
Thus, the simplified form of the radical is [tex]20x^{50}.[/tex]
