Simplify square root of 75a^2

$\sqrt{75 a^{2}}$

Step 1

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

Factor $25$ out of $75$ .

$\sqrt{25 (3) a^{2}}$

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

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

Move $3$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

$5 a \sqrt{3}$

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