Question

Siddh kijiye ki 5-3/7√3ek aparimey sankhya hai ?​

Answer 1

Given that,

A number $5-\dfrac{3}{7}\sqrt 3$ .

To prove,

The number is irrational.

Solution,

A number that can be written in the form of p/q are rational while the numbers that cannnot be written in the form of p/q are irrational.

5 is an integer, so it is a rational number

Now, taking :

$\dfrac{3}{7}\sqrt 3=\dfrac{3}{7}\times \sqrt 3$

3/7 is in the form of p/q, so it is a rational number

$\sqrt{3}$ is not an integer. So, it is an irrational number

Since, the product of rational and irrational number is always an irrational number. So, $\dfrac{3}{7}\sqrt 3$ is an irrational number.

Also, the sum of any rational number and an irrational number will always be an irrational number.

Hence, proved.