Question

proov that 7+3 root2 is not a rational number

Answer 1

Answer:

Step-by-step explanation:

LET US ASSUME ,TO THE CONTRARY , THAT 7 + 3 √2 IS RATIONAL.

THEN

                      7 + 3√2 = A/B                    

 WHERE A AND B ARE COPRIME AND  B IS NOT EQUAL TO 0 .

                            3√2 =  A-7B/B

                              √2 =   A - 7B / 3B

  FOR ANY INTEGER VALUE OF A AND B , A-7B/3B IS RATIONAL .

BUT √2 IS IRRATIONAL .

THIS CONTRADICTION HAS ARISEN DUE TO OUR INCORRECT ASSUMPTION THAT  7 + 3√2  IS RATIONAL.

HENCE  7 + 3√2 IS IRRATIONAL