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anonymous

  • one year ago

Simplify: √27 + √3

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  1. mathstudent55
    • one year ago
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    Start by simplifying \(\sqrt{27} \) Can you find two factors of 27, one of which being a perfect square?

  2. anonymous
    • one year ago
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    so the square root of 30? which would be 10 outside the square root of 3?

  3. mathstudent55
    • one year ago
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    Just like in the previous problem, \(\sqrt{48} \), 48 = 16 * 3, and 16 is a perfect square, you can rewrite 27 as the product of two numbers, one of them being a perfect square.

  4. anonymous
    • one year ago
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    10√3 so would this be the answer???

  5. mathstudent55
    • one year ago
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    No. There is no 30 here. Start with 27. Can you think of two numbers that multiply to 27 from the multiplication tables?

  6. anonymous
    • one year ago
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    9 and 3

  7. mathstudent55
    • one year ago
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    Great. Now what about 9? Is it a perfect square? Is 9 the square of some number?

  8. anonymous
    • one year ago
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    3 and 3

  9. mathstudent55
    • one year ago
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    Exactly. 9 is 3 * 3, or 3^2. Now we can continue with the problem: \(\sqrt{27} + \sqrt 3=\) \(= \sqrt{9 \times 3} + \sqrt 3\) So far we are only showing that 27 = 9 * 3 Ok?

  10. anonymous
    • one year ago
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    ok

  11. mathstudent55
    • one year ago
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    Now we can separate the numbers inside the root. \(= \sqrt{9} \times \sqrt 3 + \sqrt 3\) In the step above, all we did was to separate the root of the product 9 * 3 into the product of the roots of 9 and 3.

  12. anonymous
    • one year ago
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    yep i see so far.

  13. mathstudent55
    • one year ago
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    Now we can easily simplify \(\sqrt 9\) We know that \(\sqrt 9 = 3\), so we write 3 instead of \(\sqrt 9\): \(= 3\sqrt 3 + \sqrt 3\) On the left above you see how \(\sqrt {27} \) simplifies to \(3 \sqrt 3\)

  14. mathstudent55
    • one year ago
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    Now we need to do the addition. \(3\sqrt 3 + \sqrt 3\) Is the same as saying "what is 3 square roots of 3 added to 1 square roots of three?"

  15. anonymous
    • one year ago
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    i understand. but what answer is it?

  16. anonymous
    • one year ago
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    A. 10√3 B. 27 C. 9√3 D. 4√3

  17. mathstudent55
    • one year ago
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    What is 3x + x? What is 3 oranges plus 1 orange?

  18. anonymous
    • one year ago
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    4 oranges

  19. mathstudent55
    • one year ago
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    What is 3 of something plus one of the same thing?

  20. anonymous
    • one year ago
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    4

  21. mathstudent55
    • one year ago
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    Right, so the same way 3 square roots of 3 added to 1 square root of 3 is 4 square roots of 3. Now we can finish the problem. \(= 4 \sqrt 3\)

  22. anonymous
    • one year ago
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    oh that makes a lot more sense

  23. mathstudent55
    • one year ago
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    Here is the whole problem without the explanations in the middle: \(\sqrt{27} + \sqrt 3=\) \(= \sqrt{ 9 \times 3} + \sqrt 3\) \(=\sqrt 9 \times \sqrt 3 + \sqrt 3\) \(= 3\sqrt 3 + \sqrt 3\) \(= 4 \sqrt 3\)

  24. anonymous
    • one year ago
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    thank you! cane help me with another?

  25. anonymous
    • one year ago
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    Multiply and simplify: square root of 6 times the quantity of square root of 3 + 5 square root of 2. A. B. C.

  26. mathstudent55
    • one year ago
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    You mean this? \(\sqrt 6 \times (\sqrt 3 + 5 \sqrt 2) \)

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