Prove <msqrt> 2 </msqrt>

Alannah Short

Alannah Short

Answered question

2022-06-21

Prove 2 + 3 + 5 is an irrational number.

Answer & Explanation

svirajueh

svirajueh

Beginner2022-06-22Added 29 answers

If 2 + 3 is rational then so too is 2 3 because ( 2 + 3 ) ( 2 3 ) = 2 3 = 1
But adding the two terms, ( 2 + 3 ) + ( 2 3 ) = 2 2 which is irrational. Two rational numbers cannot sum to an irrational number so we have a contradiction. Therefore 2 + 3 is irrational. We can say 2 + 3 I and come to the same result/conclusion for + 5 .
In this case we reach the assumption that I 2 5 is rational.
But I 2 5 = ( 2 + 3 ) 2 5 = 5 + 2 6 5 = 2 6 which is irrational and another contradiction. Hence 2 + 3 + 5 is irrational.

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