#### Answer

a. $18\sqrt 3$
b. $3a^{2}* \sqrt 2$
c. $210x^{3}$
d. Yes, we can simplify to get $42t\sqrt 2t$

#### Work Step by Step

a) We can simplify as follows:
= $3\sqrt 6*\sqrt 18$
= $3*\sqrt 6*\sqrt 6*\sqrt 3$
= $3*6*\sqrt 3$
= $18\sqrt 3$
a) We can simplify as follows:
= $\sqrt 2a*\sqrt 9a^{3}$
= $\sqrt 2a*\sqrt 9*\sqrt a^{3}$
= $\sqrt 2*\sqrt a*3*\sqrt a^{2}*\sqrt a$
= $\sqrt 2*\sqrt a*3*a*\sqrt a$
= $\sqrt 2*a*3*a$
(since $\sqrt a*\sqrt a$ = a)
= $3a^{2}\sqrt 2$.
a) We can simplify as follows:
= $7\sqrt 5x*3\sqrt 20x^{5}$
= $7\sqrt 5*\sqrt x*3\sqrt 5*\sqrt 4*\sqrt x^{4}*\sqrt x$
= $7\sqrt 5*\sqrt x*3\sqrt 5* 2* x^{2}*\sqrt x$
= $7*3* 2* x^{2}*x*5$ (since $\sqrt 5 *\sqrt 5 = 5$ and $\sqrt x *\sqrt x =x$)
= $210x^{3}$
a) We can simplify as follows:
= $2\sqrt 7t*3\sqrt 14t^{2}$
= $2\sqrt 7*\sqrt t*3\sqrt 7*\sqrt 2*\sqrt t^{2}$
= $2* 7*\sqrt t*3*\sqrt 2*\sqrt t^{2}$
= $42t\sqrt 2t$.