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anonymous

  • 4 years ago

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

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  1. anonymous
    • 4 years ago
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    \[\sqrt{27}\times \sqrt{2} \]

  2. jhonyy9
    • 4 years ago
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    3sqrt3 *sqrt2 = 3sqrt6

  3. Hero
    • 4 years ago
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    = sqrt{27*2} = sqrt{54} = sqrt{9*6} = sqrt{9} * sqrt{6} = 3 sqrt{6}

  4. anonymous
    • 4 years ago
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    how did you get 3 square roots of three

  5. jhonyy9
    • 4 years ago
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    27=9*3 sqrt(9*3)=3sqrt3

  6. jhonyy9
    • 4 years ago
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    ok ?

  7. anonymous
    • 4 years ago
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    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

  8. jhonyy9
    • 4 years ago
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    yes

  9. Hero
    • 4 years ago
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    If you use my approach, you wouldn't have to worry about running into 3 sqrt{3}

  10. anonymous
    • 4 years ago
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    ok ya i think Hero's way makes a little more sence. thanks though

  11. anonymous
    • 4 years ago
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    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?

  12. anonymous
    • 4 years ago
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    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?

  13. Hero
    • 4 years ago
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    yup

  14. Hero
    • 4 years ago
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    good job

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

  16. Hero
    • 4 years ago
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    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.

  17. Hero
    • 4 years ago
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    If you multiply 12*18 you get 216. 216/6 = 36 so do sqrt{36*6}

  18. anonymous
    • 4 years ago
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    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

  19. anonymous
    • 4 years ago
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    and make it 5square roots of 6

  20. Hero
    • 4 years ago
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    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.

  21. Hero
    • 4 years ago
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    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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