Simplify

Simplify sqrt(27)*sqrt(12)*sqrt(147).  

This expression is equivalent to the       

sqrt of the product of the radicands   

sqrt(27) * sqrt(12) * sqrt(147)               =   sqrt( 27 * 12 * 147 )  

See if you can find some

perfect squares in there                        =   sqrt( 3*9 * 3*4 * 147 )  

There are two 3² and one 2²  

so take them out from under  

the radical                                              =   (3 * 3 * 2) sqrt( 147 ) 

                                                               =   18 * sqrt(147)    

_.

126$\sqrt{3}$ 

So we know that:

$\sqrt{27} * \sqrt{(12)} * \sqrt{(147)}$

( ' * ' being " multiply " )

= 42 $\sqrt{3}^3$

Simplify:

= 42 * 3$\sqrt{3}$

Multiply:

42 * 3 $\sqrt{3}$

= 126$\sqrt{3}$