Which of the following statement(s) involving square roots is or are true? I. √64 + √0.0064 + √0.81 + √0.0081 = 9.07 II. √0.010201 + √98.01 + √0.25 = 11.51

Introduction / Context:
This problem checks your comfort with square roots of whole numbers and decimals. Instead of doing heavy algebra, you simply need to evaluate each sum carefully and compare it with the given decimal value. Such questions appear in simplification and approximation sections of aptitude tests and reward precise calculation skills.

Given Data / Assumptions:

• Statement I: √64 + √0.0064 + √0.81 + √0.0081 is claimed to equal 9.07.
• Statement II: √0.010201 + √98.01 + √0.25 is claimed to equal 11.51.
• We must decide whether each statement is true or false.
• All square roots are principal (non negative) roots.

Concept / Approach:
We evaluate each square root term one by one. It helps to recognise that 0.0064, 0.81, 0.0081, 0.010201, and 98.01 are all decimals that correspond to familiar squared values. Once we convert each into its root, we add them and compare to the stated decimal. Rounding should not be needed here because the numbers are chosen to give exact results.

Step-by-Step Solution:
1. For Statement I, compute each term separately. 2. √64 = 8 because 8^2 = 64. 3. √0.0064 = 0.08 because 0.08^2 = 0.0064. 4. √0.81 = 0.9 because 0.9^2 = 0.81. 5. √0.0081 = 0.09 because 0.09^2 = 0.0081. 6. Sum them: 8 + 0.08 + 0.9 + 0.09 = 8 + 1.07 = 9.07. 7. Therefore Statement I is exactly true. 8. For Statement II, compute each square root. 9. √0.010201 = 0.101 because 0.101^2 = 0.010201. 10. √98.01 = 9.9 because 9.9^2 = 98.01. 11. √0.25 = 0.5 because 0.5^2 = 0.25. 12. Sum them: 0.101 + 9.9 + 0.5 = 10.501. 13. Statement II claims the sum is 11.51, which is clearly different from 10.501, so Statement II is false.

Verification / Alternative check:
You can quickly check Statement II in another way by estimating. Notice that √98.01 is just under 10, and the other two roots are slightly above 0.1 and 0.5 respectively. So the total must be a little above 10.6, certainly not as high as 11.51. Our more precise calculation of 10.501 fits this intuition and further confirms that only the first statement holds.

Why Other Options Are Wrong:
Option 2 (Only II) is wrong because we showed Statement II is false.
Option 3 (Both I and II) is incorrect since II fails.
Option 4 (Neither I nor II) is also wrong because Statement I is exactly true; its sum matches 9.07 without any rounding error.

Common Pitfalls:
Mistakes usually occur when squaring or square rooting decimals with multiple digits, such as confusing 0.010201 with 0.01024 or misplacing the decimal point. Another common issue is sloppy addition of the decimal results. Taking a moment to line up decimal points and to double check the square roots avoids these trivial but costly errors in a test environment.

Final Answer:
Only the first statement is correct, so the right choice is Only I.