Okay, so I need to simplify this expression: √(2.5² - 0.7²) divided by (2.7 - 2.5). Let me start by understanding each part step by step. First, I'll look at the numerator inside the square root. That's 2.5 squared minus 0.7 squared. Then the denominator is just 2.7 minus 2.5, which should be straightforward. 

Let me write down the expression again to visualize it better: √(2.5² - 0.7²) / (2.7 - 2.5). Hmm, maybe I can simplify the numerator first. Calculating 2.5 squared: 2.5 times 2.5. Let me do that. 2 times 2 is 4, 2 times 0.5 is 1, 0.5 times 2 is another 1, and 0.5 times 0.5 is 0.25. Adding those up: 4 + 1 + 1 + 0.25 = 6.25. So 2.5 squared is 6.25. 

Now, 0.7 squared. Let me compute that. 0.7 times 0.7. 7 times 7 is 49, and since there are two decimal places, it's 0.49. So 6.25 minus 0.49 is... let's see. 6.25 minus 0.4 is 5.85, then minus 0.09 more would be 5.76. So the numerator inside the square root is 5.76. 

Then the square root of 5.76. Hmm, what's the square root of 5.76? Let me think. I know that 2.4 squared is 5.76 because 2.4 times 2 is 4.8, 2.4 times 0.4 is 0.96, so 4.8 + 0.96 = 5.76. So the square root of 5.76 is 2.4. 

Now the denominator is 2.7 minus 2.5. That's straightforward. Subtracting 2.5 from 2.7 gives 0.2. So now the expression simplifies to 2.4 divided by 0.2. 

Wait, 2.4 divided by 0.2. Let me compute that. Dividing by 0.2 is the same as multiplying by 5, because 1/0.2 is 5. So 2.4 times 5. Let me calculate that. 2 times 5 is 10, 0.4 times 5 is 2, so 10 + 2 = 12. So the result is 12. 

But let me double-check each step to make sure I didn't make any mistakes. 

First step: 2.5 squared. 2.5 times 2.5. Let me confirm that again. 2 times 2 is 4, 2 times 0.5 is 1, 0.5 times 2 is 1, 0.5 times 0.5 is 0.25. Adding those: 4 + 1 + 1 + 0.25 = 6.25. Correct. 

Then 0.7 squared. 0.7 times 0.7. 7 times 7 is 49, so 0.49. Correct. 

Subtracting 0.49 from 6.25: 6.25 - 0.49. Let's do it step by step. 6.25 minus 0.4 is 5.85, then minus 0.09 is 5.76. Correct. 

Square root of 5.76. 2.4 times 2.4 is 5.76. Let me check 2.4 times 2.4. 2 times 2 is 4, 2 times 0.4 is 0.8, 0.4 times 2 is 0.8, 0.4 times 0.4 is 0.16. Adding those: 4 + 0.8 + 0.8 + 0.16 = 5.76. Correct. 

Denominator: 2.7 - 2.5. That's 0.2. Correct. 

Then 2.4 divided by 0.2. 2.4 divided by 0.2. Since 0.2 times 12 is 2.4, so yes, 12. Correct. 

Alternatively, if I convert 0.2 to a fraction, 0.2 is 1/5, so dividing by 1/5 is multiplying by 5. 2.4 times 5 is 12. Correct. 

So all steps check out. Therefore, the simplified result is 12. 

I think that's it. All steps seem correct. No mistakes detected. The answer should be 12.
Therefore, the simplified form of the given expression is $\boxed{12}$.
</think>