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let,√2+√7 is rational.
√2+√7=r ( where r is a rational no.)
on squaring both sides,
(√2+√7)=r^2
2+2√14+7=r^2
9+2√14=r^2
√14=r^2-9/2
so, r^2-9/2 is rational and rationals are closed under subtraction and division except zero..
irrational is not to rational..
so, our assumption is wrong..
hence, √2+√7 is irrational
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