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

Question

Nathan Axel · Accepted Answer

#216\sqrt{2}#

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.

Abigail Allen · Answer

undefined To simplify the expression 4*sqrt(12) * (9 sqrt(6)), we can multiply the numbers outside the square roots and combine the square roots with the same radicand.

First, we multiply 4 and 9 to get 36.

Next, we multiply the square roots of 12 and 6. The square root of 12 can be simplified as 2*sqrt(3), and the square root of 6 remains as sqrt(6).

Multiplying these square roots, we get 2*sqrt(3) * sqrt(6) = 2*sqrt(18).

Finally, we simplify the square root of 18 as 3*sqrt(2).

Therefore, the simplified expression is 36 * 3*sqrt(2), which can be further simplified as 108*sqrt(2).