Math, asked by rajeshsharma6466, 1 year ago

prove that 2√3÷5 is irrational​

Answers

Answered by Brainly100
3

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.

Similar questions