Simplify square root of 27t^2

$\sqrt{27 t^{2}}$

Step 1

Rewrite $27 t^{2}$ as ${(3 t)}^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$\sqrt{9 (3) t^{2}}$

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

$\sqrt{3^{2} \cdot 3 t^{2}}$

Move $3$ .

$\sqrt{3^{2} t^{2} \cdot 3}$

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

$\sqrt{{(3 t)}^{2} \cdot 3}$

$\sqrt{{(3 t)}^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$3 t \sqrt{3}$

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