Question

prove that 5 - 2/7√3 is irrational number.

Answer 1

Suppose 5 - 2/7√3 is rational .
Let 5 - 2/7√3= r where r is a rational. =>(5-2/7√3)^2 = r2
=>25-20√3/7 +12/49 = r2
=>√3 = (r2 - 25-12/49)/ 20*7 Now , LHS = √3 is an irrational number .
RHS(r2 - 25-12/49)/ 20*7 is a rational number .
But rational number cannot be equal to
an irrational.
our supposition is wrong.
5 - 2/7√3 is irrational .

Answer 2

Answer:

Step-by-step explanation:

Suppose 5 - 2/7√3 is rational .

Let 5 - 2/7√3= r where r is a rational. =>(5-2/7√3)^2 = r2

=>25-20√3/7 +12/49 = r2

=>√3 = (r2 - 25-12/49)/ 20*7 Now , LHS = √3 is an irrational number .

RHS(r2 - 25-12/49)/ 20*7 is a rational number .

But rational number cannot be equal to

an irrational.

our supposition is wrong.

5 - 2/7√3 is irrational .