show that√7 is rational
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let √7 be a rational number such that
√7 = a/b ... where a & b are co primes
√7 = a/b
=>7 = a²/b²
=> a²= 7b² ...(1)
=> 7 is a factor of a² as well as of b
=> a = 7K ...(2)
From (1) and (2)
49k²= 7b²
=> b²= 7k²
=> 7 is is a factor of a as well as of b
but a & b were co primes
This contradicts our assumption that √7 is rational .
Hence, √7 is irrational
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