Question

prove that 7/5√2 is irrational​

Answer 1

Step-by-step explanation:

Here let us assume that 7√2 /5 be rational . So it has co primes as a and b so, it can be expressed in the form of a/b .

$\frac{7 \sqrt{2} }{5} = \frac{a}{b} \\ = 7 \sqrt{2} = \frac{5a}{b}$

$\sqrt{2} = \frac{5a}{7b}$

Here, a and b are integers so RHS be rational.in that LHS be rational.

But, √2 is irrational.

So our contradicts arrive when we assume that 7√2/5 is rational.

7√2/5 is irrational.