lET X BE RATIONAL AND Y BE IRRATIONAL.iS XY NECESSARILY IRRATIONAL?GIVE REASONS AND JUSTIFY WITH EXAMPLE?
Asked by raoss1967 | 6th May, 2015, 12:48: PM
Yes. The product of one rational and one irrational number is an irrational number.
It can be proved by method of contradiction.
Let X be a rational number such that
Y is an irrational number such that XY=R , a rational number, where
So we get
The above conclusion is a contradiction, since Y is an irrational number.
Hence, our initial assumption that XY is rational is not true. Hence, XY is irrational. Proved.
For example, suppose X=3 and Y=√2 . XY=3√2 which is an irrational number.
Answered by satyajit samal | 7th May, 2015, 04:48: PM
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