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Prove that √3+√4 is a irrational …

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Prove that √3+√4 is a irrational number

Posted by Mithilesh Kannaujiya 4 years, 5 months ago

CBSE > Class 10 > Mathematics

2 answers

Anurag Gupta 4 years, 5 months ago

Lets assume that : √3 + √4 is rational. √3 + √4 = r , where r is rational Squaring both sides , we get [√3 + √4 ]² = r² 3 + 2√12 + 4 = r² 7 + 2√12 = r² 2√12 = r² - 6 √12 = [ r² - 6] / 2 R.H.S is purely rational , whereas , L.H.S is irrational. This is a contradiction. This means that our assumption was wrong. Hence , √3 + √4 is irrational.

Nikhil Mittal 4 years, 5 months ago

r Prove root3 + root4 is an irrational no. Mathematics 1 Answers Ramkishore Pingle Grade 10 Lets assume that : √3 + √4 is rational. √3 + √4 = r , where r is rational Squaring both sides , we get [√3 + √4 ]² = r² 3 + 2√12 + 4 = r² 7 + 2√12 = r² 2√12 = r² - 6 √12 = [ r² - 6] / 2 R.H.S is purely rational , whereas , L.H.S is irrational. This is a contradiction. This means that our assumption was wrong. Hence , √3 + √4 is irrational

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