Start with
[tex]\dfrac{\sqrt{3}}{\sqrt[4]{2}}[/tex]
Multiply and divide by the cubic root of two:
[tex]\dfrac{\sqrt{3}}{\sqrt[4]{2}}\cdot\dfrac{\sqrt[4]{2^3}}{\sqrt[4]{2^3}}[/tex]
Multiplying the fractions leads to
[tex]\dfrac{\sqrt{3}}{\sqrt[4]{2}}\cdot\dfrac{\sqrt[4]{2^3}}{\sqrt[4]{2^3}}=\dfrac{\sqrt{3}\sqrt[4]{2}}{\sqrt[4]{2\cdot 2^3}}=\dfrac{\sqrt{3}\sqrt[4]{2}}{\sqrt[4]{2^4}}=\dfrac{\sqrt{3}\sqrt[4]{2}}{2}[/tex]
