Simplify square root of 75r^3

$\sqrt{75 r^{3}}$

Step 1

Rewrite $75 r^{3}$ as ${(5 r)}^{2} \cdot (3 r)$ .

Factor $25$ out of $75$ .

$\sqrt{25 (3) r^{3}}$

Rewrite $25$ as $5^{2}$ .

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

Factor out $r^{2}$ .

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

Move $3$ .

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

Rewrite $5^{2} r^{2}$ as ${(5 r)}^{2}$ .

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

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

$5 r \sqrt{3 r}$

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