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anonymous

  • one year ago

assume that Assume a and b are nonzero rational numbers and c is an irrational number. For each of the following expressions, determine whether the result is irrational, rational, or both. Justify your answers. a(b + c) I think its irrational??

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  1. dan815
    • one year ago
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    yep

  2. anonymous
    • one year ago
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    Ok I am wondering how to explain that?

  3. dan815
    • one year ago
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    rational + irrational = irrational and constants * irrational you can think of as adding irrational to itself multiple times for example 2*irrational = irrational+irrational 3*irrational = irrational + irrational + irrational

  4. dan815
    • one year ago
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    this fits into our first 3 rules we chose

  5. dan815
    • one year ago
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    irrational + irrational = irrational rational + irrational = irrational rational+rational = rational

  6. dan815
    • one year ago
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    just prove those 3 statements to yourself and then you can use those properties and time you want

  7. anonymous
    • one year ago
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    I see. thank you I was having a hard time understanding. Thank you so much

  8. anonymous
    • one year ago
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    So if we throw a radical in there how does it change?

  9. dan815
    • one year ago
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    also another useful thing you will need for your next question sqrt(prime) = irrational the square root of a prime number is irrational you can prove this by a contradiction suppose sqrt(prime) = rational sqrt(prime)=a/b, where a and b is the lowest fraction possible meaning gcd(a,b)=1 then prime = a^2/b^2 then b^2prime=a^2 but this means there are an odd number of factors on the left and and even number of prime factors on the right this is a contradiction, ergo the srt of a prime is not rational but irrational

  10. dan815
    • one year ago
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    some of thoses steps are not obvious at first sight, you might beed to investigate some of those steps further to make sense of it

  11. anonymous
    • one year ago
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    |dw:1442966361745:dw| So this too would be irrational?

  12. dan815
    • one year ago
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    ah in this case no because you can expand the squareroot over it

  13. dan815
    • one year ago
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    heres the thing irrational^k irrational to the powers of something can be irrational or not that is a different queston

  14. anonymous
    • one year ago
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    ohh so there's a rule for that too?

  15. dan815
    • one year ago
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    |dw:1442966477052:dw|

  16. dan815
    • one year ago
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    gotta figure out the rules lol

  17. dan815
    • one year ago
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    the 3 rules i showed u earlier are just some rules i made up for you start with

  18. dan815
    • one year ago
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    because they are easy to prove and easy to use in proving other stuff

  19. dan815
    • one year ago
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    to see why we can expand like this you can write it out

  20. dan815
    • one year ago
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    |dw:1442966596867:dw|

  21. anonymous
    • one year ago
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    Gwash its so complicated. thank you so much. I am so stupid when it comes to rationals

  22. dan815
    • one year ago
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    oh dont worry its simple once u understand some more stuff

  23. dan815
    • one year ago
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    good luck

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