sum of irrational number & rational number needn't be a irrational number.

Asked by Ayan | 28th Jul, 2014, 03:51: PM

Expert Answer:

No, sum of irrational number and rational number is always irrational. 
 
Let x be irrational and r be rational. 

Assume that x + r = t is rational. Then x = t - r is the difference of two rational numbers and therefore rational. However this contradicts the assumption that x is irrational. 
Therefore x + r is irrational

Answered by Dharma Teja | 28th Jul, 2014, 06:42: PM