anonymous
  • anonymous
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??
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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dan815
  • dan815
yep
anonymous
  • anonymous
Ok I am wondering how to explain that?
dan815
  • dan815
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

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dan815
  • dan815
this fits into our first 3 rules we chose
dan815
  • dan815
irrational + irrational = irrational rational + irrational = irrational rational+rational = rational
dan815
  • dan815
just prove those 3 statements to yourself and then you can use those properties and time you want
anonymous
  • anonymous
I see. thank you I was having a hard time understanding. Thank you so much
anonymous
  • anonymous
So if we throw a radical in there how does it change?
dan815
  • dan815
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
dan815
  • dan815
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
anonymous
  • anonymous
|dw:1442966361745:dw| So this too would be irrational?
dan815
  • dan815
ah in this case no because you can expand the squareroot over it
dan815
  • dan815
heres the thing irrational^k irrational to the powers of something can be irrational or not that is a different queston
anonymous
  • anonymous
ohh so there's a rule for that too?
dan815
  • dan815
|dw:1442966477052:dw|
dan815
  • dan815
gotta figure out the rules lol
dan815
  • dan815
the 3 rules i showed u earlier are just some rules i made up for you start with
dan815
  • dan815
because they are easy to prove and easy to use in proving other stuff
dan815
  • dan815
to see why we can expand like this you can write it out
dan815
  • dan815
|dw:1442966596867:dw|
anonymous
  • anonymous
Gwash its so complicated. thank you so much. I am so stupid when it comes to rationals
dan815
  • dan815
oh dont worry its simple once u understand some more stuff
dan815
  • dan815
good luck

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