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Prove that (2 + ROOT under …

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Prove that (2 + ROOT under 3 )is irrational

Posted by Sakshi Singh 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 7 months ago

We will prove this result by contradiction method.

Let assume that {tex}( 2 + \sqrt { 3 } ){/tex} be rational.
Then 2 and {tex}\sqrt { 3 }{/tex} are rational.
{tex}\Rightarrow 2 + \sqrt { 3 } - 2{/tex} is rational ..... ({tex}\because{/tex} difference of two rational numbers is rational)
{tex}\Rightarrow \sqrt { 3 }{/tex} is rational
This contradicts the fact that {tex}\sqrt { 3 }{/tex} is irrational.
The Contradiction arises because we assume that {tex}( 2 + \sqrt { 3 } ){/tex} is rational.
Hence, {tex}2 + \sqrt { 3 }{/tex} is not a rational but an irrational number.

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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.
Ask specific question which are clear and concise.

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 Hari Anand 7 months ago

CBSE > Class 10 > Mathematics