proove that root a + root b is irrational no. if a,b are prime
Answers
Answer:
Step-by-step explanation:
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.
Answer:
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 . ... Hence a+√b is an irrational number. Hence proved
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