what is the simplified form of $sqrt{400x^{100}}$?\n$200x^{10}$\n$200x^{50}$\n$20x^{10}$\n$20x^{50}$

Explanation:

Step1: Simplify the square - root of 400

$\sqrt{400}=20$

Step2: Simplify the square - root of $x^{100}$

Using the rule $\sqrt{x^n}=x^{\frac{n}{2}}$, for $n = 100$, we have $\sqrt{x^{100}}=x^{50}$

Step3: Combine the results

$\sqrt{400x^{100}}=\sqrt{400}\times\sqrt{x^{100}} = 20x^{50}$

Answer:

$20x^{50}$