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

Question

A.4x^3square root of 2
B.8x3
C. 4x square root of 2
D.16x^3

Answer 1

To simplify the expression \(\sqrt{32x^6}\), we can break it down as follows:

1. Factor out the components inside the square root:

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

2. Simplify \(\sqrt{32}\):

   The number \(32\) can be factored as \(16 \times 2\): \[ \sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2} \]

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

   Using the property that \(\sqrt{x^n} = x^{n/2}\): \[ \sqrt{x^6} = x^{6/2} = x^3 \]

4. Combine the simplified terms:

   Now we can put it all together: \[ \sqrt{32x^6} = 4\sqrt{2} \cdot x^3 = 4x^3\sqrt{2} \]

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

\[ \boxed{4x^3\sqrt{2}} \quad \text{(Option A)} \]