Find out where Google Cloud SDK is installed

The following command will give you the information you're looking for:

$ gcloud info --format="value(installation.sdk_root)"
/path/to/google-cloud-sdk/

You need to append /bin.

You also have lots of other paths available: config.paths.global_config_dir, installation.sdk_root, and so on. Look at the output of gcloud info --format=json for all available properties to query.

I used:

dirname $(which gcloud)

And worked like a charm