Question

Let X be a rationalnumber and y be an irrational number is it necessary that XY should be an irrational

Answer 1

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→the product of irrational and rational number is always irrational

→ so XY= IRRATIONAL NUMBER

→lets proof this statement=

→ let a be an irrational number and b/c be an rational number.

→Suppose their product is rational. 

→ Then a*b/c= p/q for some rational number  p/q. 

→ Then  a=pc/qb, thus a is a rational number.

→ But this contradicts the fact that a is irrational, so a*b/c  is irrational.

HENCE PROVED

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