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Prove root 7 is irrational

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Prove root 7 is irrational

Posted by Gopika Patel 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Sneha Singh 6 years, 10 months ago

Let root 7 be a rational number Then, =√7 = a/b Now by squaring both side = (√7)² = (a/b)² = 7 = a²/b² = 7b² = a². (A²= 7b² from above) Here 7 divides a² Therefore 7 also divides a Now let a= 7c where c is some integer By squaring both sides = A² = 49c² = 7b² = 49c² = B² = 7c² Here 7 divides b² Therefore 7 also divides b Here a and b both have common factor 7 So our contradiction was wrong , Therefore √7 is irrational

0Thank You

Honey ??? 6 years, 10 months ago

First assume it that it is a rational number then your contradiction will be wrong and then you will prove it that it is irrrational and you can see in your book

1Thank You

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Posted by Hari Anand 6 months, 2 weeks ago

CBSE > Class 10 > Mathematics

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Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
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Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

Posted by Kanika . 1 month, 1 week ago

CBSE > Class 10 > Mathematics