Simplify square root of 32t^2

$\sqrt{32 t^{2}}$

Step 1

Rewrite $32 t^{2}$ as ${(4 t)}^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$\sqrt{16 (2) t^{2}}$

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

$\sqrt{4^{2} \cdot 2 t^{2}}$

Move $2$ .

$\sqrt{4^{2} t^{2} \cdot 2}$

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

$\sqrt{{(4 t)}^{2} \cdot 2}$

$\sqrt{{(4 t)}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$4 t \sqrt{2}$

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