prove that 6+√2 is an irrational number.
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Step-by-step explanation:we prove by the method of contradiction.
Let 6+√2 be a rational number and also let 6+√2=a/b here a and b are co-primes
By squaring on both sides
6+√2 whole square=a/b whole square
(6 whole square+√2whole square +2(6)(√2=a square/b square
36+4+12√2=a square/b square
40+12√2=a square/b square
There fore 12√2=a square/b square
-40
√2=1/2(a square/b square -40
Here LHS=√2 which is irrational number and RHS =1/2 (a square/b square - 40) which is rational number,but a rational number can never be equal to an irrational number
So we got contradiction
There fore 6+√2 is an irrational number
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