To delete your search activities from your Google account go to https://myactivity.google.com/?utm_source=help Sign in if prompted.
Click the three dots icon on the My Activity banner
Here you can delete an individual search entry by clicking Item view. Select the item you'd like to delete, click the three dots again, then Delete.
To delete all activities from the three dots menu select Delete activity by (click the down arrow), select All time, then Delete.