Question

prove that 3√7 is irrational​

Answer 1

HERE IS YOUR ANSWER--

Step-by-step explanation:

LET 3/(rooot7) BE RATIONAL,

SO , WE CAN SAY THAT

3×(root7)/7IS RATIONAL

IT IS OF THE FORM

PN/Q , WHERE P/Q IS RATIONAL,

SO N SHOULD ALSO BE RATIONAL

BUT WE KNOW THAT root7 IS IRRATIONAL,

SO,

IT CONTRADICTS OUR ASSUMPTIONS

HENCE,

3/(root7) IS IRRATIONAL,

HENCE PROVED

CHEERS

Answer 2

$Namste$

Hii friend,If possible , let 3✓7 be rational Number. Then 3✓7 is rational , 1/3 is rational.=> (1/3 × 3✓7) is rational.

contradiction with field axiom 1 of the reals - the axiom that the operation of addition is closed, that is ∀x,y∈R x+y∈R. therefore 3+root7 is irrational. ... All you need to know is that root 7 is irrational, because the definition of irrational is that it cannot be expressed as a fraction.