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anonymous

  • 5 years ago

consider the following radicals..

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  1. anonymous
    • 5 years ago
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    \[7\sqrt{8}+\sqrt{18}\]

  2. amistre64
    • 5 years ago
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    radicals are like variables in this case, in order to add them together they have to be "identical" can we reduce these radical expressions to have the same radical stuff?

  3. amistre64
    • 5 years ago
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    7*2sqrt(2) + 3sqrt(2) = 17sqrt(2)

  4. anonymous
    • 5 years ago
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    oh yeah, I kind of remember how these go.. but what is the next step once we square them?

  5. amistre64
    • 5 years ago
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    not squareing :) we need to get them to "look" the same: sqrt(8) = sqrt(4*2) = sqrt(4) * sqrt(2) = 2sqrt(2)

  6. amistre64
    • 5 years ago
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    sqrt(18) = sqrt(9*2) = sqrt(9) * sqrt(2) = 3sqrt(2)

  7. amistre64
    • 5 years ago
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    now we can combine these puppies since they are both "sqrt(2)"s

  8. amistre64
    • 5 years ago
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    7*2sqrt(2) + 3sqrt(2) = 14sqrt(2) + 3 sqrt(2) = 17sqrt(2)

  9. amistre64
    • 5 years ago
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    does that make sense?

  10. anonymous
    • 5 years ago
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    yeah I kind of understand where it's going. Does the *=x? ha.. i'm definitely a visual learner so that is helpful to write out. Thanks!

  11. amistre64
    • 5 years ago
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    \[\sqrt{ab} = \sqrt{a}* \sqrt{b}\]

  12. amistre64
    • 5 years ago
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    * means multiply :)

  13. anonymous
    • 5 years ago
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    gotchaa. :)

  14. amistre64
    • 5 years ago
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    \[\sqrt{8}=\sqrt{4*2}=\sqrt{4} * \sqrt{2} = 2\sqrt{2}\]

  15. anonymous
    • 5 years ago
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    would some of those cancel out then?

  16. amistre64
    • 5 years ago
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    nope, since the problem calls for addition, the only way to cancel anything out would be to subtract like amounts.

  17. anonymous
    • 5 years ago
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    wait. sorry I just realized you were giving an example. ha okk

  18. anonymous
    • 5 years ago
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    ok. So which side do we want to subtract from? Sorry, i don't know what the format of this answer should even look like really so i'm a little confused

  19. amistre64
    • 5 years ago
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    lets try this...... 7a + b = ? How would you add these together considering that they are not the same variables?

  20. amistre64
    • 5 years ago
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    we would have to redefine the variables so that they were the same.... right?

  21. anonymous
    • 5 years ago
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    yep!

  22. amistre64
    • 5 years ago
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    so, we redefine them like this: a = 2x b = 3x now: 7(2x) + 3x = ?

  23. anonymous
    • 5 years ago
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    okk

  24. amistre64
    • 5 years ago
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    14x + 3x = 17x... right? not trying to solve for x....just trying to add them together

  25. anonymous
    • 5 years ago
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    yeah. makes sense

  26. amistre64
    • 5 years ago
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    radicals act just like these variables...... we have to redefine them to "match" each other before we can add them up.

  27. amistre64
    • 5 years ago
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    \[7\sqrt{8} + \sqrt{18}\]\[7(2\sqrt{2}) + 3\sqrt{2} = ?\]

  28. amistre64
    • 5 years ago
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    now that they are the "same" variable...we can add them up\[17\sqrt{2}\]

  29. anonymous
    • 5 years ago
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    ohh cuz 2 * 7 is 14 and then we add the 3..and does it stay 2 since they are both squared 2?

  30. amistre64
    • 5 years ago
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    yep... and the so-called "variable" is the sqrt(2) part.

  31. anonymous
    • 5 years ago
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    okk thanks so much for walking through that! so the answer is \[17\sqrt{2}\]

  32. amistre64
    • 5 years ago
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    exactly :)

  33. anonymous
    • 5 years ago
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    :):)

  34. anonymous
    • 5 years ago
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    quick question..again.. to find the product for (5+3i)(5-3i) would this just be 10? I think the 3i's would cancel out?

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