Yes, you can mine Ethereum for free. The process of mining Ethereum is called “proof of work” and it involves using your computer’s processing power to solve complex mathematical problems in order to verify and add new blocks to the Ethereum blockchain.
In return for your computational power, you will be rewarded with a small amount of Ethereum.
However, mining Ethereum is not really free as you will need to pay for the electricity that your computer uses while it is mining. Additionally, if you want to be a profitable Ethereum miner you will need to invest in a powerful computer and specialized mining equipment.
Therefore, while you can mine Ethereum for free, it is not really worth it unless you are willing to make a significant investment.