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??
Stacey Warren - Expert brainly.com
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Ok I am wondering how to explain that?
rational + irrational = irrational
constants * irrational you can think of as adding irrational to itself multiple times
for example 2*irrational = irrational+irrational
3*irrational = irrational + irrational + irrational
just prove those 3 statements to yourself and then you can use those properties and time you want
thank you I was having a hard time understanding. Thank you so much
So if we throw a radical in there how does it change?
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
sqrt(prime) = rational
sqrt(prime)=a/b, where a and b is the lowest fraction possible meaning gcd(a,b)=1
prime = a^2/b^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
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
|dw:1442966361745:dw| So this too would be irrational?
ah in this case no because you can expand the squareroot over it
heres the thing irrational^k
irrational to the powers of something can be irrational or not that is a different queston
ohh so there's a rule for that too?
gotta figure out the rules lol
the 3 rules i showed u earlier are just some rules i made up for you start with
because they are easy to prove and easy to use in proving other stuff
to see why we can expand like this you can write it out
Gwash its so complicated. thank you so much. I am so stupid when it comes to rationals
oh dont worry its simple once u understand some more stuff