Answer
$15x^3y^3 \sqrt {7y}$
Work Step by Step
Use the rule $\sqrt{a}\cdot \sqrt{b}=\sqrt{ab}$, where $a,b>0$:
$\sqrt {(45)(35) \cdot x^5 \cdot x \cdot y^3 \cdot y^4}$
$=\sqrt {1575 \cdot x^5 y^3 \cdot xy^4}$
When two exponential expressions with the same base are multiplied together, add the exponents and keep the base as-is:
$=\sqrt {1575 \cdot x^6 \cdot y^7}$
Factor the radicand so that we can take the square roots later:
$=\sqrt {225(7) \cdot (x^3)^2 \cdot y^6 \cdot y}$
$=\sqrt {15^2 \cdot 7 \cdot (x^3)^2 \cdot (y^3)^2 y}$
Take the square roots:
$=15 \cdot x^3 y^3\sqrt {7 \cdot y}$
Simplify:
$=15x^3y^3 \sqrt {7y}$
