Answer
$6a^{2}b^{3}\sqrt {5a}$
Work Step by Step
Step 1: $\sqrt {12a^{3}b}\times\sqrt {15a^{2}b^{5}}$
Step 2: $\sqrt {12a^{3}b\times15a^{2}b^{5}}$
Step 3: $\sqrt {180a^{5}b^{6}}$
Step 4: $\sqrt {180}\times\sqrt {a^{5}}\times\sqrt {b^{6}}$
Step 5: $\sqrt {36\times5}\times\sqrt {a^{4}\times a}\times b^{3}$
Step 6: $6\sqrt 5\times a^{2}\sqrt a\times b^{3}$
Step 7: $6\times a^{2}\times b^{3}\times\sqrt 5\times \sqrt a$
Step 8: $6a^{2}b^{3}\sqrt {5a}$