Question

simplify the expression. assume all variables are positive real numbers. $-sqrt{\frac{p^{2}}{64}}=square$

Explanation:

Step1: Apply square - root property

We know that $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ for $a\geq0$ and $b > 0$. Here $a = p^{2}$ and $b = 64$. So, $\sqrt{\frac{p^{2}}{64}}=\frac{\sqrt{p^{2}}}{\sqrt{64}}$.

Step2: Simplify square - roots

Since $\sqrt{p^{2}}=p$ (because $p>0$) and $\sqrt{64} = 8$, then $\frac{\sqrt{p^{2}}}{\sqrt{64}}=\frac{p}{8}$.

Step3: Consider the negative sign

The original expression is $-\sqrt{\frac{p^{2}}{64}}$, so the result is $-\frac{p}{8}$.

Answer:

$-\frac{p}{8}$