Question

Rationalize the denominator.
sqrt(3)/(fourth root of 2)

Answer 1

Start with

`\frac{√(3)}{\sqrt[4]{2}}`

Multiply and divide by the cubic root of two:

`\frac{√(3)}{\sqrt[4]{2}}\cdot\frac{\sqrt[4]{2^3}}{\sqrt[4]{2^3}}`

Multiplying the fractions leads to

`\frac{√(3)}{\sqrt[4]{2}}\cdot\frac{\sqrt[4]{2^3}}{\sqrt[4]{2^3}}=\frac{√(3)\sqrt[4]{2}}{\sqrt[4]{2\cdot 2^3}}=\frac{√(3)\sqrt[4]{2}}{\sqrt[4]{2^4}}=\frac{√(3)\sqrt[4]{2}}{2}`