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Taxia2

  • one year ago

how would you solve this rational equation?

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  1. Taxia2
    • one year ago
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    \[\sqrt{15x}(\sqrt{18x}+\sqrt{15x})\]

  2. myininaya
    • one year ago
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    There is no equation to solve? Are you to multiply?

  3. Taxia2
    • one year ago
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    oops, it is supposed to be simplified!

  4. Taxia2
    • one year ago
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    but that is the equation, I have the answer, but I am unsure how to get to it.

  5. myininaya
    • one year ago
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    So we want to simplify the expression. Again there is no equation. Just so you know assuming we have x>=0 you can write \[\sqrt{18x}=\sqrt{18} \sqrt{x}\] and you can also do the same for the other terms too.

  6. myininaya
    • one year ago
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    Do you know how to multiply \[\sqrt{x} \cdot \sqrt{x}?\]

  7. Taxia2
    • one year ago
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    wouldn't that just be x?

  8. myininaya
    • one year ago
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    right another question! Do you know the distributive property?

  9. Taxia2
    • one year ago
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    I do

  10. myininaya
    • one year ago
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    so you know if you have a(b+c) you can do ab+ac

  11. myininaya
    • one year ago
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    so you have \[\sqrt{15} \sqrt{x}(\sqrt{18} \sqrt{x}+\sqrt{15} \sqrt{x})\]

  12. myininaya
    • one year ago
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    so you can treat the thing on the outside of the parenthesis just like that a above

  13. Taxia2
    • one year ago
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    yes, but wouldn't all of the square roots cancel out? I tried this but the answer i received had no square roots in it. But the answer that is given does...

  14. Taxia2
    • one year ago
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    wait, I got it!!!

  15. Taxia2
    • one year ago
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    I think...

  16. myininaya
    • one year ago
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    Is 15*18 a perfect square? I don't think it is. So you would have at least one square root in your answer. What do you think the answer is?

  17. Taxia2
    • one year ago
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    well, the given answer is \[3x \sqrt{30} +15x\] so first I simplified what i could inside the parenthesis and got \[\sqrt{15x} (3\sqrt{2x} + \sqrt{15x})\] and then I distributed (Like you said!) and got this \[3\sqrt{30x ^{2}} + \sqrt{15^{2}x ^{2}}\] then I canceled out the roots (like you said) and got the answer!

  18. myininaya
    • one year ago
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    beautiful you didn't need my help

  19. Taxia2
    • one year ago
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    I did! If I hadn't had it I probably would have given up (as cliche as that sounds) Thank you so much for working me through it!

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