Let us consider that 2/√7 is a rational number.
Let 2/√7 = a/b for b ≠ 0 ……………… (i)
Where a and b are co-prime integer numbers.
From (i) we can write as follows:
2b/a = √7
Now from the LHS we know that a and b are integral numbers and therefore the fraction will also be rational number which implies that √7 has to be a rational number. But we know that √7 is an irrational number.
So our assumption at the beginning of the problem is proved false.
So 2/√7 is an irrational number.
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