Question

Show that 2÷ 5√3 is irrational

Answer 1

Answer:

$5 \sqrt{3} \: is \: an \: irrational \: number$

2 is a rational number.

Now when a rational number is divided by an irrational number, the quotient we get is an irrational number

Step-by-step explanation:

Hope it will help.

Mark as brainliest if the answer is correct.

Answer 2

Answer:

Solution :-

To prove : 2÷5√3 is irrational

Let us assume that 2/5√3 is a rational number.

So , we can write it in the from of p/q.

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

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

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

Now , 2b/5a is a rational number which is equal to √3.

This contradict the fact that √3 is irrational. This contradiction has arise due to our incorrect assumption that 2/5√3 is rational number.

Thus , 2/5√3 is irrational.

Hope it helps you :)