Chapter A.1, Problem 40E

Solution

Rationalize the denominator.

  $\frac{2y^{3/4}}{y}$ .

Given:

The given expression is $\frac{2}{\sqrt[4]{y}}$ .

Concept Used:

• Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.
• Make sure all radicals are simplified.
• Simplify the fraction if needed.

Calculation:

The given expression is $\frac{2}{\sqrt[4]{y}}$ .

Multiply the given expression $\frac{2}{\sqrt[4]{y}}$ both numerator and denominator by $\sqrt[4]{y^3}$ .

  $\begin{array}{c}\frac{2}{\sqrt[4]{y}}=\frac{2}{\sqrt[4]{y}}\cdot \frac{\sqrt[4]{y^3}}{\sqrt[4]{y^3}}\\ =\frac{2\sqrt[4]{y^3}}{\sqrt[4]{y^4}}\\ =\frac{2{(y^3)}^{1/4}}{y}\\ =\frac{2y^{3/4}}{y}\end{array}$

Thus after rationalize the given expression $\frac{2}{\sqrt[4]{y}}$ is $\frac{2y^{3/4}}{y}$ .