Answer
$13y\sqrt{21}$.
Work Step by Step
The given expression is
$=\sqrt{7y}(\sqrt{27y}+5\sqrt{12y})$
Factor as square terms.
$=\sqrt{7y}(\sqrt{9\cdot 3y}+5\sqrt{4\cdot 3y})$
Use product property of square roots.
$=\sqrt{7y}(\sqrt{9}\cdot \sqrt{3y}+5\sqrt{4}\cdot \sqrt{3y})$
Simplify.
$=\sqrt{7y}(3 \sqrt{3y}+5\cdot 2\sqrt{3y})$
$=\sqrt{7y}(3 \sqrt{3y}+10\sqrt{3y})$
Factor out $\sqrt{3y}$.
$=\sqrt{7y}\cdot \sqrt{3y}(3+10 )$
Simplify.
$=\sqrt{7y}\cdot \sqrt{3y}(13 )$
Use product property of square roots.
$=\sqrt{7y\cdot 3y}(13)$
Simplify.
$=\sqrt{21y^2}(13)$
Use product property of square roots.
$=\sqrt{21}\cdot \sqrt{y^2}(13)$
$=\sqrt{21}\cdot y(13)$
$=13y\sqrt{21}$.
