Given xgt 0 , simplify sqrt (100x^4) completely. Answer Attemptiout of 3 square

To simplify the expression $\sqrt{100x^4}$, we can use the property of square roots that states $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$.<br /><br />First, let's break down the expression inside the square root:<br />\[ \sqrt{100x^4} = \sqrt{100 \cdot x^4} \]<br /><br />Now, apply the property of square roots:<br />\[ \sqrt{100 \cdot x^4} = \sqrt{100} \cdot \sqrt{x^4} \]<br /><br />Next, simplify each part separately:<br />\[ \sqrt{100} = 10 \]<br />\[ \sqrt{x^4} = x^2 \]<br /><br />Putting it all together:<br />\[ \sqrt{100x^4} = 10 \cdot x^2 \]<br /><br />Therefore, the simplified form of $\sqrt{100x^4}$ is:<br />\[ 10x^2 \]<br /><br />So, the final answer is:<br />\[ \boxed{10x^2} \]