First, make sure checking your Browser Version is what you are trying to do. Your Browser is just Safari or Chrome, not the whole device. If this is already up to date or you have already checked it, you might mean to be checking on your Operating System (OS) Software to see if it needs updates. Your OS is what your whole device runs on. You can learn how to check for OS Software Updates here.
Safari
Congratulations! To update the Safari on an Apple product, you only need to update your operating system. If you do not need to complete any software updates, you are good to go!
Chrome
Chrome is not as simple but still easy
Open Chrome and then click on Chrome > Settings
Then click on About Chrome and you will see if there are any updates that Chrome needs