Answer
$(9x+20)\sqrt{y}$
Work Step by Step
Simplify each radical by factoring the radicand such that one of the factors is a perfect square:
$3x\sqrt{9y}+4\sqrt{25y}\\
=3x\sqrt{9\cdot y}+4\sqrt{25\cdot y}\\
=3x\sqrt{3^2\cdot y}+4\sqrt{5^2\cdot y}\\
$
Use the rule $\sqrt{a\cdot b}=\sqrt{a} \cdot \sqrt{b}$ then simplify:
$=3x\cdot \sqrt{3^2}\cdot \sqrt{y}+4\cdot \sqrt{5^2}\cdot \sqrt{y}$
$=3x\cdot 3\cdot \sqrt{y}+4\cdot 5\cdot \sqrt{y}$
$=9x\sqrt{y}+20\sqrt{y}$
Factor out $\sqrt{y}$.
$=\sqrt{y}(9x+20)$
$=(9x+20)\sqrt{y}$
Hence, the correct answer is $(9x+20)\sqrt{y}$.
