Question

How would I simplify this radical? I have the answer but I need to know the steps taken.

Answer 1

\[3\sqrt{12} * \sqrt{6}\]

Answer 2

hint: \[\Large \sqrt{x}*\sqrt{y} = \sqrt{x*y}\]

Answer 3

\[3\sqrt{12 * 6} = 3\sqrt{72}\] Like this?

Answer 4

yes

Answer 5

now you can factor 72 in such a way where one of the factors is a perfect square

Answer 6

and then you would use that rule in reverse

Answer 7

I know that 9 times 8 is 72. Is that important?

Answer 8

you can use a larger perfect square actually

Answer 9

but you are on the right track

Answer 10

factors of 72:
1,2,3,4,6,8,9,12,18,24,36,72

Answer 11

I would factor the numbers before multiplying together. (It's easier)
\[ 3\sqrt{12} \cdot \sqrt{6} = 3 \cdot \sqrt{3\cdot 2\cdot 2}\cdot \sqrt{2\cdot 3}\]
you can combine the 2 square roots, as jim posted up above
\[ 3 \cdot \sqrt{3\cdot 2\cdot 2\cdot 2\cdot 3}\]
now look for *pairs" of numbers inside the square root, and "pull them out"
there is is pair of 3's and one pair of 2's (leaving 1 2 left over that stays inside)
when we pull out a pair, it becomes just a single number on the outside
we get
\[ 3 \cdot 3 \cdot 2 \sqrt{2} \]
or
\[ 18 \sqrt{2} \]