10. Prove that √2 + √3 is irrational.
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let assume that√2+√3 is irrational
√2+√3=a/b (here a and b are co primes)
√3=a/b-√2
(√3) ² =(a/b-√2) ² ( squaring both sides)
3=a²/b²-2a/b√2+2
2a/b√2=a²/b²-1
√2=a²-b²/2ab
since a and b are integers so a²-b²/2ab is rational
thus √2 is also rational
but this contradict the fact that√2 is irrational. so our assumption is wrong
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