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Show that √2 is irrational?

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Show that √2 is irrational?

Posted by Vivasvan Singh 7 years, 7 months ago

CBSE > Class 10 > Mathematics

2 answers

Utkarsh Patel 7 years, 7 months ago

Let √2 is irrational number ,means √2 is a rational number . Let √2= p by q √2^2= p^2 by q^2 2 = p^2 by q^2 2q^2 = p^2 -------(1) q^2=p^2 by 2 ~2 divides p^2 ~2 divides p also. Let p by 2 =r ,for some integer r. p=2r ----------(2) On substituting eq.(2) in eq.(1). 2q^2=2^2.r^2 q^2 = 4r^2 q^2=2r^2 q^2 by 2= r^2 ~2 divides q^2. ~2 divides q also Thus, is a common factor of p and q but this contradict that p and q are coprime so our assumption is wrong . Hence ,√2 is an irrational number

Utkarsh Patel 7 years, 7 months ago

Let route to be a rational number so it can be written in p by Q form where p and q are coprime numbers means it has only one factor that is 1 and where is not equal to zero

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This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

Few rules to keep homework help section safe, clean and informative.

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