prove that 7+√2 is an irrational number
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Assume that 7+√2 is rational.
∴7+√2=a/b ,where a and b are co-primes.
∴ 7+a/b=√2
√2=7b+a/b
∴ since a and b are integers 7b+a/b is rational.
√2 is also rational which contradicts the fact that √2 is irrational.
∴ our assumption is wrong.
∴7+√2 is irrational.
hence proved
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