Question

write $\frac{sqrt3{5}}{sqrt3{4}}$ as a radical expression in simplest form.
$\frac{sqrt3{5}}{sqrt3{4}} = \square$

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt[3]{2}$, since $4 \times 2 = 8 = 2^3$, which is a perfect cube.
$\frac{\sqrt[3]{5}}{\sqrt[3]{4}} \times \frac{\sqrt[3]{2}}{\sqrt[3]{2}} = \frac{\sqrt[3]{5 \times 2}}{\sqrt[3]{4 \times 2}}$

Step2: Simplify numerator and denominator

Calculate the products inside the cube roots.
$\frac{\sqrt[3]{10}}{\sqrt[3]{8}} = \frac{\sqrt[3]{10}}{2}$

Answer:

$\frac{\sqrt[3]{10}}{2}$