#### Answer

$105c\sqrt 3c$

#### Work Step by Step

Solving and simplifying the expression:
$3\sqrt 5c \times7\sqrt 15c^{2}$
= $(3\times7)(\sqrt 5c \times\sqrt 15c^{2})$
= $21(\sqrt 15 \times \sqrt 5 \times \sqrt c \times \sqrt c^{2})$
= $21(\sqrt 75 \times\sqrt c^{3})$
= $21(\sqrt 75c^{3})$
Find the square factor of $(\sqrt 75c^{3})$
$\sqrt 75c^{3} = 3 \times25 \times c^2 \times c$
=$ 3 \times5^2 \times c^2 \times c$
= $ 3c \times5^2 \times c^2 $
=$ 3c (5 c)^2 $
So $25c^2$ is its square factor
Put it in the equation:
= $21(\sqrt 3c\times\sqrt 5c^{2})$
= $21(5c \sqrt 3c )$
= $21\times 5c (\sqrt 3c) $
= $105c \sqrt 3c$