The expression 3 square root 5 * 3 square root 5^5 is equivalent to
The expression is equivalent to:
\[3\sqrt{5}\cdot (3\sqrt{5})^5 = 3\sqrt{5}\cdot 3^5 \sqrt{5^5}.\]
Since \(\sqrt{5}\cdot \sqrt{5^5} = \sqrt{(5)(5^5)} = \sqrt{5^{6}} = 5^3,\) we have
\[3\sqrt{5}\cdot 3^5 \sqrt{5^5} = 3(3^5)\cdot 5^3 = (3\cdot 3^5)\cdot 5^3 = 3^{1+5}\cdot 5^3 =\boxed{3^6\cdot 5^3}.\]