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: \[ \sqrt{64x^{9}} = 8x^{4}\sqrt{x} \]