Simplify -5/6* square root of 72p

$- \frac{5}{6} \cdot \sqrt{72 p}$

Step 1

Rewrite $72 p$ as $6^{2} \cdot (2 p)$ .

Factor $36$ out of $72$ .

$- \frac{5}{6} \cdot \sqrt{36 (2) p}$

Rewrite $36$ as $6^{2}$ .

$- \frac{5}{6} \cdot \sqrt{6^{2} \cdot 2 p}$

Add parentheses.

$- \frac{5}{6} \cdot \sqrt{6^{2} \cdot (2 p)}$

Step 2

Pull terms out from under the radical.

$- \frac{5}{6} \cdot (6 \sqrt{2 p})$

Step 3

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$\frac{- 5}{6} \cdot (6 \sqrt{2 p})$

Factor $6$ out of $6 \sqrt{2 p}$ .

$\frac{- 5}{6} \cdot (6 (\sqrt{2 p}))$

Cancel the common factor.

$\frac{- 5}{6} \cdot (6 \sqrt{2 p})$

Rewrite the expression.

$- 5 \cdot \sqrt{2 p}$

$- 5 \sqrt{2 p}$