Find the square root of a mixed number: Compute √(105 + 4/64).

Introduction / Context:
Mixed numbers often hide exact squares. Here, 4/64 simplifies to 1/16, producing a number whose square root can be found neatly.

Given Data / Assumptions:
Value = 105 + 4/64.

Concept / Approach:
Simplify 4/64 to 1/16. Recognize that 10.25^2 equals 105.0625, which matches 105 + 1/16.

Step-by-Step Solution:
4/64 = 1/16 = 0.0625.So the number is 105.0625.Compute 10.25^2 = (10 + 0.25)^2 = 100 + 2*10*0.25 + 0.25^2 = 100 + 5 + 0.0625 = 105.0625.Hence, √(105 + 1/16) = 10.25.

Verification / Alternative check:
A direct calculator check confirms 10.25^2 = 105.0625.

Why Other Options Are Wrong:
10.5, 9.75, 12.25, 15.5 do not square to 105.0625.

Common Pitfalls:
Not simplifying 4/64, or mis-squaring decimals like 10.25.

Final Answer:
10.25