Simplify 2 square root of 125v

$2 \sqrt{125 v}$

Rewrite $125 v$ as $5^{2} \cdot (5 v)$ .

Factor $25$ out of $125$ .

$2 \sqrt{25 (5) v}$

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

$2 \sqrt{5^{2} \cdot 5 v}$

Add parentheses.

$2 \sqrt{5^{2} \cdot (5 v)}$

$2 \sqrt{5^{2} \cdot (5 v)}$

Pull terms out from under the radical.

$2 (5 \sqrt{5 v})$

Multiply $5$ by $2$ .

$10 \sqrt{5 v}$

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