Ananda

Sri Sadgurubhyoh Namah 

Sat chit ananada

How to know that all beings are nothing but sat chit ananda?

I exist - sat

I know - chit

This is understood, but ananda is not experienced.

Answer: when a person has vairagya towards worldly sense pleasures, and does sadhana, his or her mind becomes peaceful, shantaha. 

A person who is shantaha experiences ananda

Shanti is ananda

Such a person is sat-chit-ananda and for that person whole world is sat chit ananda swarupa

How to know that the nature of Atma is ananda?

Answer: it is observed in the world that a person loves something which gives him/her happiness. 

And reverse is true.

It is a fact that everyone loves themselves the most. I love myself the most. It means 'myself' must be giving me happiness.

Therefore, it follows that Self must be happiness/ ananda

We like wealth and prosperity. More than that we like our family and children. More than children, we like ourselves, our body. More than our body, we like our sense organs and sense pleasures. More than that we like our life force, prana. More than that we like our Atma, Self, I am. 

In that order. This Self is the root, moolam.