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Il root a andb is an irrational number provethat root a+b is an irrational number |
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Answer» Let a+√b be a rational number. There exist two number p and q where q ≠0 and p,q are co prime i.e. p/q =a+√b Then, (p/q)² = (a+√b)² [squaring both SIDES] =› p²/q =a²+b/q ————(¹) Since p and q are co prime L.H.S. is always fractional and R.H.S. is always INTEGER . If q =1,the equation (¹) is HOLD good but it was impossible that there was no number whose square is a² +b . This is the contradiction to our assumption. Hence a+√b is an irrational number. Hence proved.
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