Show that root+ rootb is an irrational number if rootab is an irrational number.
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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.
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√3,√7,√2 ,Show that root+ rootb is an irrational number if rootab is an irrational number.
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