Simplify the Radical Expression square root of 45p^2

$\sqrt{45 p^{2}}$

Rewrite $45 p^{2}$ as ${(3 p)}^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$\sqrt{9 (5) p^{2}}$

Rewrite $9$ as $3^{2}$ .

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

Move $5$ .

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

Rewrite $3^{2} p^{2}$ as ${(3 p)}^{2}$ .

$\sqrt{{(3 p)}^{2} \cdot 5}$

Pull terms out from under the radical.

$| 3 p | \sqrt{5}$

Remove non-negative terms from the absolute value.

$3 | p | \sqrt{5}$