Question

Prove
$2 \sqrt{3} \div 5$

as
irrational​

Answer 1

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Step-by-step explanation:

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Answer 2

To prove ; 2√3 ÷ 5 is irrational

Let us assume that 2√3 ÷ 5 is an rational number

So 2√3 ÷ 5 can be written in form

$\frac{p}{q}, where, q\neq 0 ( p,q .are.co- primes)$

So,

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

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

But √3 is irrational and $\frac{5p}{2q}$ is rational.

so

2√3 ÷ 5 is irrational