While you will likely never be asked to show the proof for the least squared estimators for the simple linear regression model, I do think that there is value in having seen the proof. In this video I explain the logic behind why we minimize the sum of the squared residuals, and provide the derivation for the estimators.
NOTE: Near minute 19 I skip a step, and do not show you why Sum yi(xi - xbar) = Sum (yi - ybar)(xi - xbar), please see this video to see more details on this skipped step:
https://youtu.be/y2LiiGDIpuc