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√5 irrational |
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Answer» Sol- let, √5 be rational no. Then, it is in the form of p/q where q not equals to zero and P and q are co-prime. √5=p/q On squaring both side-5=p²/q²5q²=p² ____eqation (1)Since, 5 divides p²Therefore, 5 divides pAgain, Let, p=5cOn squaring both side, P²=25c²5q² =25c² from equation 1q² =5c²Since, 5 divides q²Therefore, 5 divides q Since, 5 is the common factor .Therefore, this contradiction Therefore, √5 is an irrational no. Yes |
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