simplify. remove all perfect squares from inside the square root. $sqrt{56z^{7}}=$

Explanation:

Step1: Factorize the number and variable part

Factorize 56 as (56 = 4\times14) and (z^{7}=z^{6}\times z). So, (\sqrt{56z^{7}}=\sqrt{4\times14\times z^{6}\times z}).

Step2: Apply square - root property (\sqrt{ab}=\sqrt{a}\cdot\sqrt{b})

(\sqrt{4\times14\times z^{6}\times z}=\sqrt{4}\cdot\sqrt{14}\cdot\sqrt{z^{6}}\cdot\sqrt{z}).

Step3: Simplify perfect - square roots

Since (\sqrt{4} = 2) and (\sqrt{z^{6}}=z^{3}), we get (2z^{3}\sqrt{14z}).

Answer:

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