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Assume √3 is a rational

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Assume √3 is a rational

Posted by Aakash .B Aakash.B 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Sabari Ram 1 year, 8 months ago

Assume √3 as irrational So, √3=p/q (Where p and q are coprime) q√3 = p S.O.B.S (squarring on bot side) q²3=p²-----"1" q²= p²\3 (remember 1.3 rule) By 1.3 p/3=c ("c" can be any positive integer) p=3c-----------"2" Now by applying EQ 2 in 1 we get, q²3=(p/3)² (p=3c) q²3=p²9 q²=p²3 q²/3=p² (recall 1.3) Our assumption is our contradiction Our assumption is wrong Hence,√3 is irrational

Aakash .B Aakash.B 1 year, 8 months ago

P/q

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