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Prove root 5 is irrational |
| Answer» Let us assume that root 5 is rational.Let p and q be real number and co primes.Now, let p and q have another factor other than 1.Now, root 5 = p/qRoot 5q= p.....................(i)(Squaring both side)Root 5q whole square = p square5q square = p squareP square is divisible by 5..Hence, p is divisible by 5..Let us take p = 5k where k is an integerFrom eq (i)...P = root 5q5k = root 5 q(Squaring both side)25k square = 5q5k square = q squareSo, q square is divisible by 5 Hence, q is divisible by 5Hence, p and q have other factors other than 1, that is 5...Hence our assumption is wrong that p and q are co primes...This contradicts the fact that root 5 is irrational.So, root 5 is irrational..This sum is looking so lengthy but its actually not..??????? | |