Question

how to solve sqrt(64x^(9))

Answer 1

To solve \( \sqrt{64x^{9}} \), we can break it down using the properties of square roots.

1. **Separate the square root**:
\[
\sqrt{64x^{9}} = \sqrt{64} \cdot \sqrt{x^{9}}
\]

2. **Calculate \( \sqrt{64} \)**:
\[
\sqrt{64} = 8
\]

3. **Simplify \( \sqrt{x^{9}} \)**:
We can use the property that \( \sqrt{x^{n}} = x^{\frac{n}{2}} \). For \( n = 9 \):
\[
\sqrt{x^{9}} = x^{\frac{9}{2}} = x^{4.5} = x^{4} \cdot \sqrt{x}
\]

4. **Combine the results**:
Putting it all together, we have:
\[
\sqrt{64x^{9}} = 8 \cdot x^{4} \cdot \sqrt{x}
\]

Thus, the final answer is:
\[
\sqrt{64x^{9}} = 8x^{4}\sqrt{x}
\]