Let's break down the expression step by step using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right)):

Given:
\[
5 - 7 \times 8 + \frac{14}{1} - \frac{53}{25} - 7 \times \sqrt{164}
\]

### Step 1: Handle multiplication and division from left to right

- \( 7 \times 8 = 56 \)
- \( \frac{14}{1} = 14 \)
- \( \frac{53}{25} \approx 2.12 \)
- \( \sqrt{164} \approx 12.81 \), so \( 7 \times \sqrt{164} \approx 89.67 \)

Now the expression becomes:
\[
5 - 56 + 14 - 2.12 - 89.67
\]

### Step 2: Perform addition and subtraction from left to right

- \( 5 - 56 = -51 \)
- \( -51 + 14 = -37 \)
- \( -37 - 2.12 = -39.12 \)
- \( -39.12 - 89.67 = -128.79 \)

Thus, the final result is approximately:
\[
\boxed{-128.79}
\]

Would you like more details or have any further questions?

Here are five related questions to explore:
1. How do you apply the order of operations (PEMDAS) in complex expressions?
2. How does understanding square roots help in simplifying expressions?
3. What is the difference between exact and approximate values in calculations?
4. Can you explore other methods for simplifying multi-step equations?
5. How can rounding affect the accuracy of your final result?

**Tip**: Always apply the order of operations consistently to avoid errors in complex expressions.

5 − 7 ∗ 8 + 14 ÷ 1 − 53 ÷ 25 − 7 ∗ √164 =

Learn how to solve the mathematical expression 5 − 7 * 8 + 14 ÷ 1 − 53 ÷ 25 − 7 * √164 using the order of operations (PEMDAS). This detailed solution covers square roots, multiplication, division, addition, and subtraction, suitable for students in Grades 8-10.

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