Simplify square root of z/64

$\sqrt{\frac{z}{64}}$

Step 1

Rewrite $\frac{z}{64}$ as ${(\frac{1}{8})}^{2} z$ .

Factor the perfect power $1^{2}$ out of $z$ .

$\sqrt{\frac{1^{2} z}{64}}$

Factor the perfect power $8^{2}$ out of $64$ .

$\sqrt{\frac{1^{2} z}{8^{2} \cdot 1}}$

Rearrange the fraction $\frac{1^{2} z}{8^{2} \cdot 1}$ .

$\sqrt{{(\frac{1}{8})}^{2} z}$

Step 2

Pull terms out from under the radical.

$\frac{1}{8} \sqrt{z}$

Step 3

Combine $\frac{1}{8}$ and $\sqrt{z}$ .

$\frac{\sqrt{z}}{8}$