Question

what is the simplified form of the following expression?
$25xy\sqrt{\frac{81}{625}x^{2}y^{2}}$
$\bigcirc\\ \frac{9}{25}|xy|$
$\bigcirc\\ \frac{9}{625}x^{2}y^{2}$
$\bigcirc\\ 9xy|xy|$
$\bigcirc\\ 9x^{2}y^{2}$

Explanation:

Step1: Split the square root

$\sqrt{\frac{81}{625}x^2y^2} = \sqrt{\frac{81}{625}} \cdot \sqrt{x^2} \cdot \sqrt{y^2}$

Step2: Compute each square root

$\sqrt{\frac{81}{625}} = \frac{9}{25}$, $\sqrt{x^2}=|x|$, $\sqrt{y^2}=|y|$

Step3: Multiply with the outside term

$25xy \cdot \frac{9}{25}|x||y| = 9xy|x||y|$

Step4: Simplify the product

$9xy|x||y| = 9xy|xy|$

Answer:

$9xy|xy|$ (matches the third option: $9xy|xy|$)