Q. 593 - Intermediate Algebra

Question

In the following exercises, simplify. Assume all variables are positive.

$\frac{\sqrt{245x{y}^{-4}}}{\sqrt{45x^{-4}{y}^3}}$

Step-by-Step Solution

Answer

The simplified expression is $\frac{7x^3}{3y}\times \sqrt{\frac{x}{y}}$

Step 1. Given Information

We have $\frac{\sqrt{245x{y}^{-4}}}{\sqrt{45x^{-4}{y}^3}}$

Step 2. Factor the Radicand

$$\begin{gathered} \frac{\sqrt{245x{y}^{-4}}}{\sqrt{45x^{-4}{y}^3}}=\frac{\sqrt{5\times 7\times 7\times x\times x^4}}{\sqrt{3\times 3\times 5\times y^3\times y^4}} \\ =\frac{7x^2\sqrt{5}\sqrt{x}}{3\times y\times y^2\sqrt{5}\sqrt{y}} \end{gathered}$$

Step 3. Simplify the expression

$$\begin{gathered} \frac{7x^2}{3y}\times \frac{\sqrt{5}}{\sqrt{5}}\times \sqrt{\frac{x}{y}} \\ =\frac{7x^3}{3y}\times \sqrt{\frac{x}{y}} \end{gathered}$$