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

1 Answer
flamespirit919
Apr 27, 2017

216\sqrt{2}216√2

Explanation:

First, simplify sqrt{12}√12. We know that 12=4\cdot312=4⋅3 and \sqrt{4}=2√4=2. So we can say that \sqrt{12}=\sqrt{4\cdot 3}√12=√4⋅3 or \sqrt{12}=\sqrt{4}\cdot\sqrt{3}√12=√4⋅√3. This then simplifies to 2\sqrt{3}2√3.

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

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

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

We know that 18=9\cdot 218=9⋅2 so we can do the following
\sqrt{18}=\sqrt{9\cdot 2}=3\sqrt{2}√18=√9⋅2=3√2

72\cdot 3\sqrt{2}72⋅3√2
=216\sqrt{2}=216√2

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

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