Question

is the sum of two irrational numbers always irrational? justify your answer.

Answer 1

no, sum of two irrationals need but be irrational always.
example: √2 and -√2 are irrationals
their sum: √2+(-√2)=√2-√2=0
zero is rational number.
hence, justified.


hope it helps.
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Answer 2

No , the sum of two irrational numbers are not always irrational

Given : The sum of two irrational numbers always irrational

To find : Justify the answer

Solution :

We know that Rational number is defined as a number of the form $\displaystyle \sf{ \frac{p}{q} \: }$ Where p & q are integers with q ≠ 0

For example let us take two irrational numbers 2 + √3 & 2 - √3

The sum

= 2 + √3 + 2 - √3

= 4 which is rational

Next let us take two irrational numbers 2 + √5 & 2 - √3

The sum

= 2 + √5 + 2 - √3

= 4 + √5 - √3 which is irrational

Hence we can conclude that the sum of two irrational numbers are not always irrational

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