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
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
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