P
√ ___
64
= p
___
8
Is that right?
Is this what you're trying to simplify?
$\displaystyle \sqrt{\frac{p}{64}}$?
If so, you've made a mistake.
You use the index law $\displaystyle \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.
Since a surd is a fractional power, we can use this index law for surds as well.
$\displaystyle \sqrt{\frac{p}{64}}=\frac{\sqrt{p}}{\sqrt{64}} = \frac{\sqrt{p}}{8}$.