Question

please explain me that what is irrational no & how to prove it in detail​

Answer 1

Answer:Any repeating/recouring/non-terminating decimal number is a irrational number They are represented by P or Q'.Like 1.98749874... and 1.45364536... etc

The are roots of a non perfect square i.e, - 2 roots,3root,5root etc.

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

A number which cannot be expressed in the form of p/q where p and q are integers and q is not equal to 0 is called irrational number

If we want to prove a given no irrational the following are the steps

Let's take how to prove root 3 as irrational no

Let's us assume root 3 as rational

Root3= a/ b where a and b are co- primes , no common factor other than 1

Root 3 b = a

Squaring on both sides we get

3 b ^2 = a ^2

Therefore 3 divides a

Now let's us take

a=3c where c is some integer

Squaring on both sides

a^2 =9 c^2

But a^2 = 3b^2

Therefore

3b^2 = 9c^2

b^2 = 3c^2

3 divides b

As 3 divides both a and b our assumption is wrong that a and b are co- primes

Therefore root 3 is irrational

Hope this helps u ????!!!