Evaluate \(\sqrt ( \frac { 0.0961} { 4.0836- 3.7112} ) \) , correct to four decimal places, hence write the answer in the right form. 

1. Calculate the denominator:
   \[4.0836 - 3.7112 = 0.3724\]
2. Divide the numerator by the denominator:
   \[\frac { 0.0961} { 0.3724} \approx 0.2581\]
3. Take the square root of the result:
   \[\sqrt { 0.2581} \approx 0.5080\]

Supplemental Knowledge

When simplifying expressions that contain square roots, it's crucial to follow an order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (such as powers and square roots), Multiplication/Division from left-to-right as well as Addition and Subtraction respectively.

1. Evaluate the expression inside the parentheses first:
   • Calculate \(4.0836 - 3.7112\).
2. Divide the numerator by the result from step 1:
   • Divide \(0.0961\) by the result obtained in step 1.
3. Take the square root of the quotient:
   • Find \(\sqrt { \text { result from step 2} } \).

Real-World Applications

Learning how to simplify expressions is critical in various fields like physics or engineering where precise calculations are essential for designing systems or solving issues.
If your project involves calculating electrical resistance or thermal conductivity, for instance, then simplifying similar expressions accurately might be essential to success.

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