Simplify 5 square root of 80a^2

$5 \sqrt{80 a^{2}}$

Step 1

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

Factor $16$ out of $80$ .

$5 \sqrt{16 (5) a^{2}}$

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

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

Move $5$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

$5 (4 a \sqrt{5})$

Step 3

Multiply $4$ by $5$ .

$20 a \sqrt{5}$

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