-2[5+ ( 3+4 )²+∛-125

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Introduction

In this article, we will delve into the world of mathematics and explore a complex expression that involves various mathematical operations. The expression -2[5+ ( 3+4 )²+∛-125] requires a deep understanding of mathematical concepts such as exponents, roots, and order of operations. We will break down the expression step by step and provide a clear explanation of each operation.

Understanding the Expression

The given expression is -2[5+ ( 3+4 )²+∛-125]. To solve this expression, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Step 1: Evaluate the Expression Inside the Parentheses

The first step is to evaluate the expression inside the parentheses, which is ( 3+4 )². To do this, we need to follow the order of operations.

  • Evaluate the expression inside the parentheses: 3+4 = 7
  • Raise 7 to the power of 2: 7² = 49

So, the expression inside the parentheses is equal to 49.

Step 2: Evaluate the Expression Inside the Square Root

The next step is to evaluate the expression inside the square root, which is ∛-125. To do this, we need to find the cube root of -125.

  • Find the cube root of -125: ∛-125 = -5

So, the expression inside the square root is equal to -5.

Step 3: Evaluate the Expression Inside the Brackets

Now that we have evaluated the expressions inside the parentheses and the square root, we can evaluate the expression inside the brackets.

  • Add 5 and 49: 5 + 49 = 54
  • Add 54 and -5: 54 + (-5) = 49

So, the expression inside the brackets is equal to 49.

Step 4: Multiply the Result by -2

The final step is to multiply the result by -2.

  • Multiply 49 by -2: -2 × 49 = -98

So, the final result is -98.

Conclusion

In this article, we have solved a complex mathematical expression that involves various mathematical operations. We have followed the order of operations and broken down the expression step by step to arrive at the final result. The expression -2[5+ ( 3+4 )²+∛-125] requires a deep understanding of mathematical concepts such as exponents, roots, and order of operations. We hope that this article has provided a clear explanation of how to solve this expression.

Mathematical Operations Used

  • Parentheses: Used to group expressions and follow the order of operations.
  • Exponents: Used to raise a number to a power.
  • Square Root: Used to find the square root of a number.
  • Cube Root: Used to find the cube root of a number.
  • Multiplication: Used to multiply two numbers.
  • Addition: Used to add two numbers.
  • Subtraction: Used to subtract one number from another.

Real-World Applications

The mathematical operations used in this expression have real-world applications in various fields such as:

  • Science: Used to calculate distances, velocities, and accelerations.
  • Engineering: Used to design and build structures, machines, and systems.
  • Finance: Used to calculate interest rates, investments, and returns.
  • Computer Science: Used to develop algorithms and programs.

Tips and Tricks

  • Follow the order of operations: To avoid errors and ensure accuracy.
  • Use parentheses: To group expressions and follow the order of operations.
  • Use exponents: To raise a number to a power.
  • Use square roots: To find the square root of a number.
  • Use cube roots: To find the cube root of a number.
  • Use multiplication: To multiply two numbers.
  • Use addition: To add two numbers.
  • Use subtraction: To subtract one number from another.

Conclusion

Introduction

In our previous article, we explored the complex mathematical expression -2[5+ ( 3+4 )²+∛-125] and broke it down step by step to arrive at the final result. In this article, we will answer some frequently asked questions about this expression and provide additional insights and explanations.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is crucial to avoid errors and ensure accuracy in mathematical calculations. If you don't follow the order of operations, you may get incorrect results, which can lead to serious consequences in fields like science, engineering, and finance.

Q: What is the difference between a square root and a cube root?

A: A square root is a mathematical operation that finds the number that, when multiplied by itself, gives a specified value. For example, the square root of 16 is 4, because 4 × 4 = 16. A cube root, on the other hand, is a mathematical operation that finds the number that, when cubed (multiplied by itself three times), gives a specified value. For example, the cube root of 27 is 3, because 3 × 3 × 3 = 27.

Q: How do I evaluate expressions with exponents?

A: To evaluate expressions with exponents, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions (e.g., 2^3). Finally, evaluate any multiplication and division operations from left to right.

Q: What is the significance of the expression -2[5+ ( 3+4 )²+∛-125]?

A: The expression -2[5+ ( 3+4 )²+∛-125] is a complex mathematical expression that involves various mathematical operations. The expression is significant because it requires a deep understanding of mathematical concepts such as exponents, roots, and order of operations. The expression also has real-world applications in fields like science, engineering, finance, and computer science.

Q: How do I apply the order of operations to this expression?

A: To apply the order of operations to this expression, follow these steps:

  1. Evaluate the expression inside the parentheses: ( 3+4 )² = 49
  2. Evaluate the expression inside the square root: ∛-125 = -5
  3. Add 5 and 49: 5 + 49 = 54
  4. Add 54 and -5: 54 + (-5) = 49
  5. Multiply 49 by -2: -2 × 49 = -98

Q: What are some real-world applications of the mathematical operations used in this expression?

A: The mathematical operations used in this expression have real-world applications in various fields such as:

  • Science: Used to calculate distances, velocities, and accelerations.
  • Engineering: Used to design and build structures, machines, and systems.
  • Finance: Used to calculate interest rates, investments, and returns.
  • Computer Science: Used to develop algorithms and programs.

Conclusion

In this article, we have answered some frequently asked questions about the complex mathematical expression -2[5+ ( 3+4 )²+∛-125] and provided additional insights and explanations. We hope that this article has provided a clear understanding of the order of operations and the significance of this expression.