Finding the least possible sum of a product.

[Physics345]

Homework Statement

The product of two positive numbers is 100. What numbers will produce the least possible sum? Confirm that the sum is in fact a minimum.

Homework Equations

The Attempt at a Solution

For this question here I feel like the wording is a bit confusing, I tried my best please let me know if I'm on the right track and if there is any mistakes we can work through.
Anyways here's my train of thought:
From my understanding it is asking me to find two positive numbers that have a product of 100. Basically two numbers when multiplied together equal 100, and the two numbers need to have the lowest possible sum when added together.
Here's my work:

 

[DrClaude]

What you posted is a bit hard to follow (it doesn't appear to be first column followed by second column, but rather some back and forth), but overall it appears correct.

 

[Physics345]

What you posted is a bit hard to follow (it doesn't appear to be first column followed by second column, but rather some back and forth), but overall it appears correct.

That is true, I'll be sure to put the math in order from now on. I wrote that when I first woke up. I wasn't thinking straight, it looks like I'm still doing math in my dreams, which is also extremely unorganized/confusing but correct.
I appreciate your help kind sir.

 

[Mark44]

Thread moved to Calc & Beyond section.