Simplify square root of 80p^3

$\sqrt{80 p^{3}}$

Step 1

Rewrite $80 p^{3}$ as ${(4 p)}^{2} \cdot (5 p)$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5) p^{3}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 5 p^{3}}$

Factor out $p^{2}$ .

$\sqrt{4^{2} \cdot 5 (p^{2} p)}$

Move $5$ .

$\sqrt{4^{2} p^{2} \cdot 5 p}$

Rewrite $4^{2} p^{2}$ as ${(4 p)}^{2}$ .

$\sqrt{{(4 p)}^{2} \cdot 5 p}$

Add parentheses.

$\sqrt{{(4 p)}^{2} \cdot (5 p)}$

$\sqrt{{(4 p)}^{2} \cdot (5 p)}$

Step 2

Pull terms out from under the radical.

$4 p \sqrt{5 p}$

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