Examine whether root 2 is rational or irrational number
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irrational number...
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root 2 = p/q where p and q are co primes as we assumed that root 2 is irrational
2 = p^2/q^2 ........ 2[q^2] = p^2
therefore p divides 2
p = 2m as 2 is divisible by p
p^2 = 4[m^2]
2[q^2] = 4[m^2] as p^2 = 2[q^2]
q^2 = 2[m^2]
therefore q also divides 2
but this contradicts the fact that p and q are co primes
therefore root 2 is irrational
2 = p^2/q^2 ........ 2[q^2] = p^2
therefore p divides 2
p = 2m as 2 is divisible by p
p^2 = 4[m^2]
2[q^2] = 4[m^2] as p^2 = 2[q^2]
q^2 = 2[m^2]
therefore q also divides 2
but this contradicts the fact that p and q are co primes
therefore root 2 is irrational
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