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Prove √5 as irrational

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Prove √5 as irrational

Posted by Pratyay Samanta 7 years, 7 months ago

CBSE > Class 10 > Mathematics

2 answers

Khushboo Deshmukh 7 years, 7 months ago

Proof = (contradiction method ) Let √5 is a rational P/q=√5 (p and q coprime) Square both sides P2 /q2 = 5 P2 = 5 q2 equations (1) 5 divides p2 5 divides p equation (2) Let p= 5 M Square both sides P2=25M2 Put p2 =5q2 from eq (1) 5 q2 = 25 m2 q2=25m2/5 q2=5m2 5 divides q2 5 divide q (3) From (1) and (3) 5 is factor of both p and q P and q are not coprime ( from equation (1) ) This is contradiction of our assumption P and q are coprime So, our assumption is wrong Hence, √5 is a irrational Proved

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Deeksha Kalyan 7 years, 7 months ago

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Posted by Kanika . 1 month, 1 week ago

CBSE > Class 10 > Mathematics