+0  
 
0
71
3
avatar

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

 Apr 28, 2023
 #1
avatar
0

 

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)    

 

.

 Apr 28, 2023
 #2
avatar
0

 

CONTINUED FROM ABOVE  

 

too late to edit my above   

 

I noticed another square  

 

SUBSTITUTE THE FOLLOWING

 

See if you can find some

perfect squares in there                        =   sqrt( 3*9 * 3*4 * 3*49 )  

 

There are two 32, one 22,  

and one 72, so take them

out from under the radical                     =   (3 * 3 * 2 * 7) sqrt( 3 ) 

 

                                                              =  126 * sqrt(3)   

.

Guest Apr 28, 2023
 #3
avatar+135 
+1

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\(\sqrt{3}\)

 Apr 28, 2023

1 Online Users