If p is the prime positive …
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Sia ? 2 years, 10 months ago
For any prime positive integer p, √p is an irrational number.
Let us assume that √p is a rational number.
Then, there exist positive co-primes a and b such that :-
√p = a/b
p = a²/b²
b²p = a²
p divide a²
p divides a.
a = pc ( positive integer c. )
Now, b²p = a²
b²p = p²c²
b² = pc²
p divide b²
p divides b
Therefore, p/a and p/b
This contradicts the fact that a and b are co-primes.
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