Question

prove that 2√3÷5 is irrational​

Answer 1

Prove that following is Irrational

$\frac{2 \sqrt{3} }{5}$

ANSWER

Let the number be Rational.

Then It can be written as p/q , where p and q are rational.

$\frac{2 \sqrt{3} }{5} = \frac{p}{q} \\ \\ \\ \implies 2 \sqrt{3} = \frac{5 p}{q} \\ \\ \\ \implies \sqrt{3} = \frac{5p}{2q}$

Now, if p is rational then 5p is also rational similarly 2q ia rational and a rational number by a rational number is also rational.

Hence, RHS is rational but LHS is irrational because root 3 is irrational.

So it contradicts our assumtion the given number is irrational.