# How do you rationalize the denominator and simplify 4sqrt(7/(2z^2))?

$\textcolor{b l u e}{4 \sqrt{\frac{7}{2 {z}^{2}}} = \frac{2 \sqrt{14}}{z}}$

$\textcolor{red}{\sqrt[4]{\frac{7}{2 {z}^{2}}} = \frac{\sqrt[4]{56 {z}^{2}}}{2 z}}$

#### Explanation:

If the given is to simplify 4sqrt(7/(2z^2)

The solution:

$4 \sqrt{\frac{7}{2 {z}^{2}}} = 4 \sqrt{\frac{7}{2 {z}^{2}} \cdot \frac{2}{2}} = 4 \sqrt{\frac{14}{4 {z}^{2}}} = \frac{4 \sqrt{14}}{2 z} = \frac{2 \sqrt{14}}{z}$

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If the given is to simplify $\sqrt[4]{\frac{7}{2 {z}^{2}}}$

The solution:

$\sqrt[4]{\frac{7}{2 {z}^{2}}} = \sqrt[4]{\frac{7}{2 {z}^{2}} \cdot \left(\frac{8 {z}^{2}}{8 {z}^{2}}\right)} = \sqrt[4]{\frac{56 {z}^{2}}{16 {z}^{4}}} = \frac{\sqrt[4]{56 {z}^{2}}}{2 z}$

God bless....I hope the explanation is useful.