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Prove that 2 root under 3 …

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Prove that 2 root under 3 - 1 is an irrational number

Posted by Rohit Kumar 6 years, 10 months ago

CBSE > Class 10 > Mathematics

3 answers

Khushboo Giri 6 years, 10 months ago

if your Q is 2√3-1 then, Let 2√3-1 be rational number say p/q where q is not equal to zero and p and q are coprime. 2√3-1=p/q 2√3=p/q+1 √3=p+q/2q √3is irrational and p+q/2q is rational. But rational is not equal to irrational. Therefore 2√3-1 is irrational.

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Khushboo Giri 6 years, 10 months ago

2√3-1 2√2 Let 2√2 be rational number say p/q where q is not equal to zero and p&q are coprime. 2√2=p/q √2=p/q÷2 √2 is irrational and p/q÷2 is rational. But rational is not equal to irrational. Therefore 2√2 is irrational.

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Affu 😊 6 years, 10 months ago

Let 2√3-1 is rational , let a and b is the positive integer , 2√3-1=a/b , 2√3=a/b+1 , 2√3= a+b/b , √3=a+b/2b , so our assumption was wrong , hence 2√3-1 is irrational

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