Simplify square root of 448x^2

$\sqrt{448 x^{2}}$

Step 1

Rewrite $448 x^{2}$ as ${(8 x)}^{2} \cdot 7$ .

Factor $64$ out of $448$ .

$\sqrt{64 (7) x^{2}}$

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} \cdot 7 x^{2}}$

Move $7$ .

$\sqrt{8^{2} x^{2} \cdot 7}$

Rewrite $8^{2} x^{2}$ as ${(8 x)}^{2}$ .

$\sqrt{{(8 x)}^{2} \cdot 7}$

$\sqrt{{(8 x)}^{2} \cdot 7}$

Step 2

Pull terms out from under the radical.

$8 x \sqrt{7}$

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