Question

Simplify Expressions -

$\frac{\sqrt{180p^5{q}^2}}{\sqrt{3p^3{q}^6}}$

Short answer

The simplification of Expression will be - $\frac{2p}{q^2}\sqrt{15}$

Step-by-step solution

Step 1.  Given Data

Expressions -

$\frac{\sqrt{180p^5{q}^2}}{\sqrt{3p^3{q}^6}}$

Step 2.  To Find

Simplify The Expressions.

Step 3.  Explanation

Expression - $\frac{\sqrt{180p^5{q}^2}}{\sqrt{3p^3{q}^6}}$

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

localid="1648572747746" $$\begin{gathered} \frac{\sqrt{180p^5{q}^2}}{\sqrt{3p^3{q}^6}} \\ \sqrt{\frac{180p^5{q}^2}{3p^3{q}^6}} \end{gathered}$$

Step 4.  Calculation

Remove common factors in the numerator and denominator.

$$\begin{gathered} \sqrt{\frac{180p^5{q}^2}{3p^3{q}^6}} \\ \sqrt{\frac{60\times 3\times p^3\times p^2\times q^2}{3\times p^3\times q^2\times q^4}} \\ \sqrt{\frac{60p^2}{q^4}} \end{gathered}$$

Simplify -

$$\begin{gathered} \sqrt{\frac{60p^2}{q^4}} \\ \frac{2p}{q^2}\sqrt{15} \end{gathered}$$