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- anonymous

simplify the expression square root of 27 times square root of 2

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- anonymous

simplify the expression square root of 27 times square root of 2

- jamiebookeater

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- anonymous

\[\sqrt{27}\times \sqrt{2} \]

- jhonyy9

3sqrt3 *sqrt2 = 3sqrt6

- Hero

= sqrt{27*2}
= sqrt{54}
= sqrt{9*6}
= sqrt{9} * sqrt{6}
= 3 sqrt{6}

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- anonymous

how did you get 3 square roots of three

- jhonyy9

27=9*3
sqrt(9*3)=3sqrt3

- jhonyy9

ok ?

- anonymous

so take the perfact square of 9 out of 27 so 9 times 3 =27 then the suare root of 9 is 3 so 3 suare roots of the 3 that cant be simplified right

- jhonyy9

yes

- Hero

If you use my approach, you wouldn't have to worry about running into 3 sqrt{3}

- anonymous

ok ya i think Hero's way makes a little more sence. thanks though

- anonymous

so 27 times 2 =54 than take the perfect square root of 9 out so 9 times 6= 54 then simplify so 3 square roots of 6 corect?

- anonymous

so as another example \[\sqrt{10} \times \sqrt{8}\] 10 times 8 is 80 then take 16 out so 16 times 5 = 80 then simplify to 4 square roots of 5 is that how it works?

- Hero

yup

- Hero

good job

- anonymous

ok but what about \[\sqrt{12} \times \sqrt{18}\] i have a fealing theres an extra step i don't know how to do

- Hero

It's the same strategy...look for the highest square, then split it up into a square root of two numbers, one being a square.

- Hero

If you multiply 12*18 you get 216.
216/6 = 36
so do sqrt{36*6}

- anonymous

i got 18 times 12 is 216 then 9 times 24 so 3 is from the 9 and the 24 also can go to 4times 6 which is 2 square roots of 6 so would i add 3+ 2

- anonymous

and make it 5square roots of 6

- Hero

Basically, there are two strategies to finding the square. You either divide by multiples of two until you find a square, or you divide by squares until you get a non-decimal integer.

- Hero

Basically, I did this:
216/2 no
216/4 no
216/6 yes
Or you can find the nearest square and divide by that like so:
216/196 no
216/169 no
...
216/36 yes
It depends on which number you're working with but either way works.

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