Chapter 9.3, Problem 8Q

To determine

To Simplify: The expression $\sqrt{\frac{4x^2}{28y^4{z}^5}}$

Answer to Problem 8Q

The required answer is $\frac{x\sqrt{7z}}{7y^2{z}^3}$ .

Explanation of Solution

Given information:

The expression $\sqrt{\frac{4x^2}{28y^4{z}^5}}$

Calculation:

  $\begin{array}{l}\sqrt{\frac{4x^2}{28y^4{z}^5}}\\ =\sqrt{\frac{2^2\cdot x^2}{2^2\cdot 7y^4{z}^{4}z}}\\ =\frac{2x}{2y^2{z}^2}\sqrt{\frac{1}{7z}}\end{array}$

Rationalize the denominator

  $\begin{array}{l}=\frac{2x}{2y^2{z}^2}\sqrt{\frac{1}{7z}}\cdot \frac{\sqrt{7z}}{\sqrt{7z}}\\ =\frac{x\sqrt{7z}}{y^2{z}^2\cdot 7z}\\ =\frac{x\sqrt{7z}}{7y^2{z}^3}\end{array}$