Which expression is equivalent to square root of 32x^6

Answer 1

To simplify the expression \(\sqrt{32x^6}\), we can break it down into simpler parts.

1. Start with the square root of the product:

   \[ \sqrt{32x^6} = \sqrt{32} \cdot \sqrt{x^6} \]

2. Next, simplify \(\sqrt{32}\). We can factor \(32\) into \(16 \cdot 2\):

   \[ \sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2} \]

3. Now simplify \(\sqrt{x^6}\):

   \[ \sqrt{x^6} = x^{6/2} = x^3 \]

4. Combine these results:

   \[ \sqrt{32x^6} = 4\sqrt{2} \cdot x^3 \]

Putting it all together, we get:

\[ \sqrt{32x^6} = 4x^3\sqrt{2} \]

Thus, the expression equivalent to \(\sqrt{32x^6}\) is:

\[ 4x^3\sqrt{2} \]