Chapter 9.2, Problem 47E

To determine

The expression which represents the given term in simplest form

Answer to Problem 47E

  $I.\frac{3\sqrt{x}}{y}$

Explanation of Solution

Given:

The given expression is

  $\sqrt{\frac{9x}{y^2}}$

Calculation:

The expression can be simplified as:

  $\begin{array}{l}=\sqrt{\frac{9x}{y^2}}\\ =\frac{\sqrt{9x}}{\sqrt{y^2}}\\ =\frac{{\left(3\times 3\right)}^{\frac{1}{2}}{\left(x\right)}^{\frac{1}{2}}}{{\left(y^2\right)}^{\frac{1}{2}}}\\ =\frac{{\left(3^2\right)}^{\frac{1}{2}}{\left(x\right)}^{\frac{1}{2}}}{{\left(y^2\right)}^{\frac{1}{2}}}\\ =\frac{3\sqrt{x}}{y}\end{array}$

Option I. $\frac{3\sqrt{x}}{y}$ correctly represents the expression $\sqrt{\frac{9x}{y^2}}$ .