Simplify square root of 56z^7

$\sqrt{56 z^{7}}$

Rewrite $56 z^{7}$ as ${(2 z^{3})}^{2} \cdot (14 z)$ .

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Factor $4$ out of $56$ .

$\sqrt{4 (14) z^{7}}$

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

$\sqrt{2^{2} \cdot 14 z^{7}}$

Factor out $z^{6}$ .

$\sqrt{2^{2} \cdot 14 (z^{6} z)}$

Rewrite $z^{6}$ as ${(z^{3})}^{2}$ .

$\sqrt{2^{2} \cdot 14 ({(z^{3})}^{2} z)}$

Move $14$ .

$\sqrt{2^{2} {(z^{3})}^{2} \cdot 14 z}$

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

$\sqrt{{(2 z^{3})}^{2} \cdot 14 z}$

Add parentheses.

$\sqrt{{(2 z^{3})}^{2} \cdot (14 z)}$

Pull terms out from under the radical.

$2 z^{3} \sqrt{14 z}$

Simplify square root of 56z^7

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