1.

(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

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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