Question

for which value of x does \\(\sqrt{x}\\) simplify to \\(20\sqrt{2}\\) ? \\(\circ\\) 800 \\(\circ\\) 400 \\(\circ\\) 40 \\(\circ\\) 22

Explanation:

Step1: Set up the equation

We know that $\sqrt{x}=20\sqrt{2}$. To find $x$, we square both sides of the equation.

Step2: Square both sides

Squaring the left side gives $(\sqrt{x})^2 = x$. Squaring the right side, we use the property $(ab)^2 = a^2b^2$. So, $(20\sqrt{2})^2 = 20^2\times(\sqrt{2})^2$.

Step3: Calculate the right side

First, $20^2 = 400$ and $(\sqrt{2})^2 = 2$. Then, multiply these results: $400\times2 = 800$. So, $x = 800$.

Answer:

800 (corresponding to the option with 800)