Question

Show that 3√7 is an irrational number

Answer 1

let us suppose that 3√7 is a rational number

so 3√7= a/b which are coprime number

√7=a/3b

√7=intergers/3×integers

√7 is a rational number

which contradicts our Statment so 3√7 is a irrational number

Answer 2

HLO FRND HERE IS UR ANSWER FRND...

LET US TAKE ON CONTRARY THAT 3√7 IS RATIONAL.

THEN THERE EXIST TWO CO PRIME NUMBERS, a AND b SUCH THAT

3√7=a/b

→√7=a/3b

NOW LHS IS AN IRRATIONAL NUMBER

WHEREAS RHS IS RATIONAL.

THIS CONTRADICTION HAS ARISED DUE TO OUR WRONG ASSUMPTION IN BEGINNING. THEREFORE 3√7 IS AN IRRATIONAL NUMBER.

HOPE IT'S HELP YOU.