Question

Prove 2√5/3 is irrational

Answer 1

Answer:

let us assume that

$2 \sqrt{ \frac{5}{3} } is \: rational$

then, we can write -

$2 \sqrt{ \frac{5}{3 \: } } = \frac{a}{b}$

or,

$\sqrt{ \frac{5}{3 \: } } = \frac{a}{b \times 2}$

or, Since RHS is rational, so LHS is also rational I.e,

$\sqrt{ \frac{5}{3} } \: \: is \: rational$

or,

$2 \sqrt{ \frac{5}{3 \: } } \: is \: rational$

A contradiction.

Hence, our assumptions is wrong.

therefore-

$2 \sqrt{ \frac{5}{3 \: } } \: is \: irrational$