How do you simplify root3(5/64)?

$\frac{1}{2} \setminus \sqrt[5]{\frac{5}{2}}$

Explanation:

$\setminus \sqrt[5]{\frac{5}{64}}$

$= \setminus \sqrt[5]{\frac{5}{2 \setminus \cdot {2}^{5}}}$

$= \setminus \sqrt[5]{\left(\frac{5}{2}\right) \left(\frac{1}{2} ^ 5\right)}$

$= \setminus \sqrt[5]{\frac{5}{2}} \setminus \sqrt[5]{\frac{1}{2} ^ 5}$

$= \setminus \sqrt[5]{\frac{5}{2}} \frac{1}{\setminus} \sqrt[5]{{2}^{5}}$

$= \setminus \sqrt[5]{\frac{5}{2}} \setminus \cdot \frac{1}{2}$

$= \frac{1}{2} \setminus \sqrt[5]{\frac{5}{2}}$

Aug 3, 2018

$\frac{\sqrt[3]{5}}{4}$

Explanation:

$\sqrt[3]{\frac{5}{64}}$

$\therefore = \frac{\sqrt[3]{5}}{\sqrt[3]{64}}$

$\therefore = \frac{\sqrt[3]{5}}{\sqrt[3]{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2}}$

$\therefore = \sqrt[3]{a} \cdot \sqrt[3]{a} \cdot \sqrt[3]{a} = a$

$\therefore = \frac{\sqrt[3]{5}}{4}$

~~~~~~~~~~~~

$\therefore \sqrt[3]{\frac{5}{64}} = 0.427493986 \text{by calculator}$

$\therefore \frac{\sqrt[3]{5}}{4} = 0.427493986 \text{by calculator}$

Aug 3, 2018

$\frac{\sqrt[3]{5}}{4}$, or ${5}^{\frac{1}{3}} / 4$

Explanation:

We can rewrite this as

$\frac{\sqrt[3]{5}}{\sqrt[3]{64}}$

Since $5$ isn't a perfect cube, we cannot simplify the numerator further, but recall that

${4}^{3} = 64$. With this in mind, $\sqrt[3]{64}$ simplifies to $4$, and we're left with

$\frac{\sqrt[3]{5}}{4}$, which can be alternatively written as ${5}^{\frac{1}{3}} / 4$.

Hope this helps!