Question

Simplify. Assume z is greater than zero. radical 63 / 28z^8

Answer 1

To simplify the expression \(\frac{\sqrt{63}}{28z^8}\), let's break it down step by step:

1. **Simplify \(\sqrt{63}\)**:
\[
63 = 9 \times 7 = 3^2 \times 7
\]
Therefore,
\[
\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7}
\]

2. **Substitute back into the expression**:
\[
\frac{\sqrt{63}}{28z^8} = \frac{3\sqrt{7}}{28z^8}
\]

3. **Simplify the fraction**:
Next, we'll simplify \(\frac{3}{28}\):
\[
\frac{3\sqrt{7}}{28z^8} = \frac{3}{28} \cdot \frac{\sqrt{7}}{z^8}
\]

4. **Final expression**:
The simplified expression is:
\[
\frac{3\sqrt{7}}{28z^8}
\]

Thus, the final simplified result is:
\[
\frac{3\sqrt{7}}{28z^8}
\]