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(ii)7JF(iii) 6+./2(iv)3. Prove that S+ 3 is irrational.4. If p,q are prime positive integers, prove that Vp+ V5.is aProve that 3+J4 is an irrational number |
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Answer» 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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