Checkpoint: Rationalizing Denominators Solution

Simplify. Rationalize the denominator

$\frac{4 x}{\sqrt[4]{2}}$

$\frac{4 x}{\sqrt[4]{2}} (\frac{\sqrt[4]{2^{3}}}{\sqrt[4]{2^{3}}}) \frac{4 x \sqrt[4]{2^{3}}}{2} = \frac{{}^{2}4 x \sqrt[4]{8}}{2} = 2 x \sqrt[4]{8}$

Note

Q: What is the index of the radical?

A: 4

Q: Why is the index important when rationalizing the denominator?

A: This helps determine what term will be multiplied by the numerator and denominator so that the radical simplifies out of the denominator.