Question

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

Answer 1

Start with

$\dfrac{\sqrt{3}}{\sqrt[4]{2}}$

Multiply and divide by the cubic root of two:

$\dfrac{\sqrt{3}}{\sqrt[4]{2}}\cdot\dfrac{\sqrt[4]{2^3}}{\sqrt[4]{2^3}}$

Multiplying the fractions leads to

$\dfrac{\sqrt{3}}{\sqrt[4]{2}}\cdot\dfrac{\sqrt[4]{2^3}}{\sqrt[4]{2^3}}=\dfrac{\sqrt{3}\sqrt[4]{2}}{\sqrt[4]{2\cdot 2^3}}=\dfrac{\sqrt{3}\sqrt[4]{2}}{\sqrt[4]{2^4}}=\dfrac{\sqrt{3}\sqrt[4]{2}}{2}$