Question

please solve it
Prove that 6+√2 is irrational​

Answer 1

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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