Maths1210
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A student argues that when a rational number is multiplied by an irrational number the result will always be an irrational number.

Identify the rational number for which the students argument is not true.

Could someone explain how to do this question please?
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the bear
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there is only one rational number which when multiplied by an irrational number makes a rational number....

you need to think about it.
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Maths1210
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(Original post by the bear)
there is only one rational number which when multiplied by an irrational number makes a rational number....

you need to think about it.
Would it be zero?
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the bear
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(Original post by Maths1210)
Would it be zero?
yes.

https://s3-eu-west-1.amazonaws.com/s...23/XJyemeI.jpg
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Maths1210
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How would I prove that the student is right for all rational numbers except zero.

Ive started by assuming qy is rational and qy = a/b where b doesn't equal zero but don't know where to go from there.
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the bear
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they are not asking you to prove the result, just to state it.
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Maths1210
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#7
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Part b of the question asks me to prove it
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the bear
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let us call the irrational number W

let us call the rational number we are multiplying by a/b and the rational product c/d

=====> aW/b = c/d

=====> W = (bc)/(ad)

can you continue ?
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Maths1210
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(Original post by the bear)
let us call the irrational number W

let us call the rational number we are multiplying by a/b and the rational product c/d

=====> aW/b = c/d

=====> W = (bc)/(ad)

can you continue ?
Im confused on whats going on
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the bear
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(Original post by Maths1210)
Im confused on whats going on
we are multiplying a rational number a/b by an irrational number W. the answer, we are told, is rational, so i have called it c/d.

now i have rearranged to get W as the subject.
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