#### Answer

$3^{20}x^{51}y^8\times\sqrt{3y}$

#### Work Step by Step

$\sqrt{3^{41}x^{102}y^{17}}$
Factor out even powers.
$\sqrt{(3)(3^{40})(x^{102})(y)(y^{16})}$
Use the Product Property of Square Roots.
$\sqrt{3^{40}}\times\sqrt{3}\times\sqrt {x^{102}}\times\sqrt y\times\sqrt{y^{16}}$
Simplify square roots with variables to even powers.
$3^{20}\times\sqrt3\times x^{51}\times\sqrt y \times y^8$
Use the Product Property of Square Roots.
$3^{20}x^{51}y^8\times\sqrt{3y}$