Question

Simplify Expressions -

$\frac{\sqrt{98r{s}^{10}}}{\sqrt{2r^3{s}^4}}$

Short answer

The simplification of Expression will be -$\frac{7s^3}{r}$

Step-by-step solution

Step 1.  Given Data

Expressions -

$\frac{\sqrt{98r{s}^{10}}}{\sqrt{2r^3{s}^4}}$

Step 2.  To Find

Simplify The Expressions.

Step 3.  Explanation

Expressions - $\frac{\sqrt{98r{s}^{10}}}{\sqrt{2r^3{s}^4}}$

Neither radicand is a perfect square, so rewrite using the quotient property of square roots -

localid="1648573311567" $$\begin{gathered} \frac{\sqrt{98r{s}^{10}}}{\sqrt{2r^3{s}^4}} \\ \sqrt{\frac{98r{s}^{10}}{2r^3{s}^4}} \end{gathered}$$

Step 4.  Calculation

Remove common factors in the numerator and denominator.

$$\begin{gathered} \sqrt{\frac{98r{s}^{10}}{2r^3{s}^4}} \\ \sqrt{\frac{2\times 49\times r\times s^4\times s^6}{2\times r\times r^2\times s^4}} \\ \sqrt{\frac{49s^6}{r^2}} \end{gathered}$$

Simplify -

$$\begin{gathered} \sqrt{\frac{49s^6}{r^2}} \\ \frac{7s^3}{r} \end{gathered}$$