The Square Root That Changed Everything

By Mario Alexandre March 30, 2026 6 min read ExamplesSelf Realization

Just a Square Root

A client gave me a prompt. Take a number they enter, find its square root, then use that number as a base price for a set of properties. I read it and thought: easy. One math function, one multiplication, done. Five minutes, maybe ten.

I was very wrong. Not because the math was hard. Because I was mixing up the math with the whole project around it.

What I Actually Discovered

The square root itself is one line of code. But the system around it needs dozens of decisions. What happens if the client types a negative number? What if they type zero? How many decimal places does the answer need? Is it rounded or cut off? How does the base price connect to the property list? Is it multiplied, divided, or used as a percentage?

Who decides the pricing formula? A mathematician. Who builds the screen where the client types their number? A designer. Who writes the code that sends the number to the math engine? A backend engineer. Who checks that the mathematician and the engineer built the same thing? A project manager. Who handles testing and keeping it running? Another engineer.

Five people. For one square root.

What This Taught Me About Prompting

I had been sending prompts with this same hidden mess inside them. Every prompt I called "simple" was really five prompts squeezed into one sentence. The AI got that one sentence and had to figure out all five on its own. It did not know which role to play. It did not know which step came first. It did not know what rules to follow.

The AI tried its best. But without clear direction, the result was just okay. Not because the AI is weak. Because my prompt left out too much.

That square root taught me to break things apart first. Now, before I write any prompt, I list the roles. I list the steps. I list the rules. Then I write the prompt. The breakdown comes first. The prompt comes second. The results are clear because the input was clear.

Nothing Is Simple

I do not trust the word "simple" anymore when it comes to prompts. Every task that looks easy on the outside has a structure hiding inside. That structure must be spelled out. The AI can only work with what I give it. If I give it a vague one-liner, I get a vague answer. If I give it the full structure, I get the full solution.

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