How do you simplify #4*sqrt(12) * (9 sqrt(6))#?

1 Answer
Apr 27, 2017

Answer:

#216\sqrt{2}#

Explanation:

First, simplify #sqrt{12}#. We know that #12=4\cdot3# and #\sqrt{4}=2#. So we can say that #\sqrt{12}=\sqrt{4\cdot 3}# or #\sqrt{12}=\sqrt{4}\cdot\sqrt{3}#. This then simplifies to #2\sqrt{3}#.

Now we have
#4\cdot 2\sqrt{3}\cdot 9\sqrt{6}#

We can simplify this to
#8\sqrt{3}\cdot 9\sqrt{6}#

Multiplying these two we get
#72\sqrt{18}#

We know that #18=9\cdot 2# so we can do the following
#\sqrt{18}=\sqrt{9\cdot 2}=3\sqrt{2}#

#72\cdot 3\sqrt{2}#
#=216\sqrt{2}#

Since 2 is a prime number, we can't simplify anymore.