Answer: The required simplified form is 20 × 10.
Step-by-step explanation: We are given to find the simplified form of the following radical expression :
[tex]E=\sqrt{400\times 100}.[/tex]
We will be using the following property of radicals :
[tex](i)~\sqrt{x}=x^\frac{1}{2}\\\\(ii)~\sqrt{a\times b}=\sqrt a\times\sqrt b.[/tex]
Therefore, we have
[tex]E\\\\=\sqrt{400\times 100}\\\\=\sqrt{400}\times\sqrt{100}\\\\=\sqrt{20^2}\times\sqrt{10^2}\\\\=((20)^2)^\frac{1}{2}\times(10^2)^\frac{1}{2}\\\\=20^{2\times\frac{1}{2}}\times(10)^{2\times\frac{1}{2}}\\\\=20\times10.[/tex]
Thus, the required simplified form is 20 × 10.
