Possible to get the V8 JavaScript engine version number in JavaScript in Chrome

Not directly via Javascript no, but you could map each Chrome version to the V8 engine.

To find the v8 version that Chrome is using, simply look it up using the URI: chrome://version/

This is not possible in Chrome. For interest though, in the Node.js runtime, you can get this in Javascript under process.versions.v8 - for example, console.log(process.versions.v8)

You can parse Chrome version from User Agent string

console.log(window.navigator.userAgent);

    "Mozilla/5.0 (Windows NT 6.1; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/71.0.3578.98 Safari/537.36"

console.log(window.navigator.userAgent.match(/Chrome\/(\d+).\d+.\d+.\d+/)[1]);

    "71"

This means, your v8 version is 7.1, because it always corresponds to a Chrome release number.

This is not too reliable as one can change its User Agent string either manually or automatically (e.g. via Chrome extension), but still usable in simple cases.