Is there a method for finding two irrational numbers that multiply together to form a rational number

Hallie Stanton

Hallie Stanton

Answered question

2022-11-18

Is there a method for finding two irrational numbers that multiply together to form a rational number

Answer & Explanation

luluna81mxmbk

luluna81mxmbk

Beginner2022-11-19Added 17 answers

If you want w v = r where w , v are irrational and r is rational, that must mean that w = r v (since v is irrational it isn't 0 so we don't have to worry about that)
So to find any pair you want just pick any arbitrary rational number (so long as it is not zero; as w 0 and v 0 then w v 0; but that is the only restriction; we can pick any other rational at all), and pick any arbitrary irrational v. Then let w = r v . As v is irrational and r is non-zero rational we will have w = r v be irrational.
And we have, voila w v = r v v = r.

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