Let's break down the expression and solve it step by step. The expression you provided is:

$((17100 \times 0.85 \times 1) \times (0.237 - 0) / 2.1315) \times (0.237 - 0) / (0.237 - 0) + (0.643 \times 0.3249 \times ((2.1315 \times (0.237 - 0))^{0.5}))$

Step 1: Simplify individual terms

• $17100 \times 0.85 = 14535$
• $0.237 - 0 = 0.237$
• $2.1315 \times 0.237 = 0.505$

So the expression now looks like this: $((14535 \times 0.237) / 2.1315) \times 0.237 / 0.237 + (0.643 \times 0.3249 \times (0.505^{0.5}))$

Step 2: Simplify the first part

$14535 \times 0.237 = 3442.395$ $3442.395 / 2.1315 = 1614.975$ $1614.975 \times 0.237 / 0.237 = 1614.975$

Step 3: Simplify the second part

$0.505^{0.5} = \sqrt{0.505} \approx 0.7107$ $0.643 \times 0.3249 = 0.2089$ $0.2089 \times 0.7107 = 0.1487$

Step 4: Combine both parts

$1614.975 + 0.1487 = 1615.1237$

Thus, the result of the given expression is approximately 1615.12.

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Would you like any further details or clarifications on the steps? Here are some related questions:

1. How do square roots and powers affect the results of equations like this?
2. Can you explain the importance of order of operations (PEMDAS) in simplifying expressions?
3. What are the different ways to approach complex algebraic expressions?
4. How can I use a calculator to check the accuracy of such expressions?
5. What does the operation $(a-b)$ represent in this context, and why is it used so often?

Tip: When dealing with complex expressions, break them down into smaller parts and simplify step by step to avoid mistakes!