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shaniehh
 one year ago
A student is attempting to show that the product of a nonzero rational number and an irrational number is always rational or always irrational.
shaniehh
 one year ago
A student is attempting to show that the product of a nonzero rational number and an irrational number is always rational or always irrational.

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shaniehh
 one year ago
Best ResponseYou've already chosen the best response.0Part A: Find the value of \[0.22 \] * \[\sqrt{112}\]and place it in simplified form.

shaniehh
 one year ago
Best ResponseYou've already chosen the best response.0Part B: Is the answer in Part A irrational or rational? Make a conjecture about the product of a nonzero rational number and an irrational number.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not really clear what the question is find the value of what?

shaniehh
 one year ago
Best ResponseYou've already chosen the best response.0I need help with part B the answer to A is 2.32826115

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it just says "make a conjecture" but the truth is that a rational number times an irrational number is always irrational

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the proof is very simple if you want to see it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a rational number is any number that can be expressed as a fraction (ratio of two integers) an irrational number is one that cannot be expressed that way we need to know this to start

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0perhaps the easiest way to show that the product of an irrational number and a rational number is irrational is to prove it by contradiction, that is, assume that the product IS rational, then get a contradiction

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so suppose \(a\) is rational, \(b\) is irrational and \(ab=c\) is rational that means that \(b=\frac{c}{a}\) is irrational, but since both \(c\) and \(a\) are rational so is \(\frac{c}{a}\) contradicting the fact that \(b\) if irrational

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0btw if this seems like kicking the can down the road, it is not you can prove for yourself that if \(c, a\) are rational, then so is \(\frac{c}{a}\) by writing them both as the ratio of two integers, invert and multiply to get another ratio of two integers
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