Simplify The Expression: 49 + − 8 3 − ( − 4 ) 3 \sqrt{49} + \sqrt[3]{-8} - (-4)^3 49 + 3 − 8 − ( − 4 ) 3
Introduction
In this article, we will simplify the given mathematical expression: . This expression involves various mathematical operations, including square roots, cube roots, and exponentiation. Our goal is to simplify this expression by performing the necessary calculations and applying the rules of arithmetic operations.
Understanding the Components
Before we dive into simplifying the expression, let's break down each component and understand what it represents.
- Square Root: The square root of a number is a value that, when multiplied by itself, gives the original number. In this expression, we have , which represents the square root of 49.
- Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In this expression, we have , which represents the cube root of -8.
- Exponentiation: Exponentiation is a mathematical operation that involves raising a number to a power. In this expression, we have , which represents -4 raised to the power of 3.
Simplifying the Expression
Now that we have a good understanding of the components involved, let's simplify the expression step by step.
Step 1: Simplify the Square Root
The square root of 49 is a value that, when multiplied by itself, gives 49. We know that 7 multiplied by 7 gives 49, so the square root of 49 is 7.
import math
square_root = math.sqrt(49)
print(square_root) # Output: 7
Step 2: Simplify the Cube Root
The cube root of -8 is a value that, when multiplied by itself three times, gives -8. We know that -2 multiplied by -2 multiplied by -2 gives -8, so the cube root of -8 is -2.
cube_root = -2
print(cube_root) # Output: -2
Step 3: Simplify the Exponentiation
The expression represents -4 raised to the power of 3. To simplify this, we need to multiply -4 by itself three times.
exponentiation = (-4) * (-4) * (-4)
print(exponentiation) # Output: -64
Step 4: Combine the Simplified Components
Now that we have simplified each component, let's combine them to simplify the original expression.
simplified_expression = 7 + (-2) - (-64)
print(simplified_expression) # Output: 69
Conclusion
In this article, we simplified the given mathematical expression: . We broke down each component, understood what it represents, and then simplified each component step by step. Finally, we combined the simplified components to get the final result. The simplified expression is 69.
Final Answer
The final answer is .
Additional Resources
For more information on mathematical operations, including square roots, cube roots, and exponentiation, please refer to the following resources:
Related Articles
Introduction
In our previous article, we simplified the mathematical expression: . We broke down each component, understood what it represents, and then simplified each component step by step. In this article, we will answer some frequently asked questions related to the simplification of mathematical expressions.
Q&A
Q: What is the square root of 49?
A: The square root of 49 is 7, because 7 multiplied by 7 gives 49.
Q: What is the cube root of -8?
A: The cube root of -8 is -2, because -2 multiplied by -2 multiplied by -2 gives -8.
Q: What is the exponentiation of (-4)^3?
A: The exponentiation of (-4)^3 is -64, because -4 multiplied by -4 multiplied by -4 gives -64.
Q: How do I simplify a mathematical expression with multiple components?
A: To simplify a mathematical expression with multiple components, you need to break down each component, understand what it represents, and then simplify each component step by step. Finally, you can combine the simplified components to get the final result.
Q: What are some common mathematical operations that I should know?
A: Some common mathematical operations that you should know include:
- Addition: Adding two or more numbers together.
- Subtraction: Subtracting one number from another.
- Multiplication: Multiplying two or more numbers together.
- Division: Dividing one number by another.
- Square Root: Finding the value that, when multiplied by itself, gives the original number.
- Cube Root: Finding the value that, when multiplied by itself three times, gives the original number.
- Exponentiation: Raising a number to a power.
Q: How do I use Python to simplify a mathematical expression?
A: You can use Python to simplify a mathematical expression by using the math module. For example, you can use the sqrt function to find the square root of a number, and the pow function to raise a number to a power.
import math
square_root = math.sqrt(49)
print(square_root) # Output: 7
exponentiation = math.pow(-4, 3)
print(exponentiation) # Output: -64
Conclusion
In this article, we answered some frequently asked questions related to the simplification of mathematical expressions. We covered topics such as square roots, cube roots, exponentiation, and using Python to simplify mathematical expressions. We hope that this article has been helpful in clarifying any doubts you may have had.
Final Answer
The final answer is .
Additional Resources
For more information on mathematical operations, including square roots, cube roots, and exponentiation, please refer to the following resources:
Related Articles
Note: The above related articles are fictional and not actual articles.