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Prove that √3+√4 is a irrational number |
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Answer» Lets assume that :√3 + √4 is rational.√3 + √4 = r , where r is rationalSquaring both sides , we get[√3 + √4 ]² = r²3 + 2√12 + 4 = r²7 + 2√12 = r²2√12 = r² - 6√12 = [ r² - 6] / 2R.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. rProve root3 + root4 is an irrational no.Mathematics\xa01 AnswersRamkishore PingleGrade 10Lets assume that :√3 + √4 is rational.√3 + √4 = r , where r is rationalSquaring both sides , we get[√3 + √4 ]² = r²3 + 2√12 + 4 = r²7 + 2√12 = r²2√12 = r² - 6√12 = [ r² - 6] / 2R.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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