Which is a simpler form of sqrt (36g^6) 36g^3 36g^4 6g^3 6g^4

To simplify the expression $\sqrt{36g^6}$, 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 />\[<br />\sqrt{36g^6} = \sqrt{36 \cdot g^6}<br />\]<br /><br />Next, we can separate the square root into two parts:<br />\[<br />\sqrt{36 \cdot g^6} = \sqrt{36} \cdot \sqrt{g^6}<br />\]<br /><br />Now, we simplify each part separately:<br />\[<br />\sqrt{36} = 6<br />\]<br />\[<br />\sqrt{g^6} = g^3 \quad \text{(since } \sqrt{g^6} = g^{6/2} = g^3\text{)}<br />\]<br /><br />Putting it all together, we get:<br />\[<br />\sqrt{36g^6} = 6 \cdot g^3 = 6g^3<br />\]<br /><br />Therefore, the simplified form of $\sqrt{36g^6}$ is:<br />\[<br />\boxed{6g^3}<br />\]