Simplify The Expression: 2 7 + 3 7 − 4 7 2 \sqrt{7} + 3 \sqrt{7} - 4 \sqrt{7} 2 7 + 3 7 − 4 7

Mar 8, 2025 by ADMIN 100 views

$Simplify the Expression: $2 \sqrt{7} + 3 \sqrt{7} - 4 \sqrt{7}$$

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems more efficiently. When dealing with expressions containing square roots, it's essential to understand how to combine like terms and simplify the expression. In this article, we will focus on simplifying the expression $2 \sqrt{7} + 3 \sqrt{7} - 4 \sqrt{7}$ .

Understanding the Expression

The given expression is a combination of three terms, each containing a square root of 7. The terms are $2 \sqrt{7}$ , $3 \sqrt{7}$ , and $-4 \sqrt{7}$ . To simplify this expression, we need to combine like terms, which means adding or subtracting terms that have the same variable and exponent.

Combining Like Terms

When combining like terms, we add or subtract the coefficients of the terms. In this case, the coefficients are the numbers in front of the square root. The expression can be rewritten as:

2 \sqrt{7} + 3 \sqrt{7} - 4 \sqrt{7} = (2 + 3 - 4) \sqrt{7}

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression further. The expression inside the parentheses is $2 + 3 - 4$ , which equals $1$ . Therefore, the simplified expression is:

1 \sqrt{7} = \sqrt{7}

Conclusion

In conclusion, simplifying the expression $2 \sqrt{7} + 3 \sqrt{7} - 4 \sqrt{7}$ involves combining like terms and simplifying the resulting expression. By following the steps outlined in this article, we can simplify the expression to $\sqrt{7}$ .

Real-World Applications

Simplifying expressions is a crucial skill in mathematics, and it has many real-world applications. In physics, for example, simplifying expressions is essential for solving problems involving motion, energy, and momentum. In engineering, simplifying expressions is necessary for designing and analyzing complex systems.

Tips for Simplifying Expressions

Here are some tips for simplifying expressions:

Combine like terms: When combining like terms, add or subtract the coefficients of the terms.
Simplify the expression: Once you have combined like terms, simplify the resulting expression by canceling out any common factors.
Use the order of operations: When simplifying expressions, use the order of operations (PEMDAS) to ensure that you are performing the operations in the correct order.

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying expressions:

Not combining like terms: Failing to combine like terms can lead to incorrect answers.
Not simplifying the expression: Failing to simplify the expression can lead to unnecessary complexity.
Not using the order of operations: Failing to use the order of operations can lead to incorrect answers.

Final Thoughts

Simplifying expressions is a crucial skill in mathematics, and it has many real-world applications. By following the steps outlined in this article, we can simplify the expression $2 \sqrt{7} + 3 \sqrt{7} - 4 \sqrt{7}$ to $\sqrt{7}$ . Remember to combine like terms, simplify the expression, and use the order of operations to ensure that you are performing the operations in the correct order.

Additional Resources

For more information on simplifying expressions, check out the following resources:

Mathway: A math problem solver that can help you simplify expressions.
Khan Academy: A free online resource that provides video lessons and practice exercises on simplifying expressions.
Math Open Reference: A free online reference book that provides information on simplifying expressions.

Frequently Asked Questions

Here are some frequently asked questions about simplifying expressions:

Q: What is the difference between combining like terms and simplifying an expression? A: Combining like terms involves adding or subtracting terms that have the same variable and exponent. Simplifying an expression involves canceling out any common factors and reducing the expression to its simplest form.
Q: How do I know when to combine like terms? A: You should combine like terms when you have two or more terms that have the same variable and exponent.
Q: What is the order of operations? A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an expression. The order of operations is: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Introduction

In our previous article, we discussed how to simplify the expression $2 \sqrt{7} + 3 \sqrt{7} - 4 \sqrt{7}$ . In this article, we will provide a Q&A section to help you better understand the concept of simplifying expressions.

Q&A

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms involves adding or subtracting terms that have the same variable and exponent. Simplifying an expression involves canceling out any common factors and reducing the expression to its simplest form.

Q: How do I know when to combine like terms?

A: You should combine like terms when you have two or more terms that have the same variable and exponent.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an expression. The order of operations is: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: Can I simplify an expression with variables?

A: Yes, you can simplify an expression with variables. However, you need to follow the same rules as before: combine like terms and simplify the expression.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you need to follow the same rules as before: combine like terms and simplify the expression. Additionally, you can simplify fractions by canceling out any common factors.

Q: Can I simplify an expression with negative numbers?

A: Yes, you can simplify an expression with negative numbers. However, you need to follow the same rules as before: combine like terms and simplify the expression.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, you need to follow the same rules as before: combine like terms and simplify the expression. Additionally, you can simplify exponents by canceling out any common factors.

Q: Can I simplify an expression with radicals?

A: Yes, you can simplify an expression with radicals. However, you need to follow the same rules as before: combine like terms and simplify the expression.

Q: How do I simplify an expression with absolute values?

A: To simplify an expression with absolute values, you need to follow the same rules as before: combine like terms and simplify the expression. Additionally, you can simplify absolute values by canceling out any common factors.

Q: Can I simplify an expression with complex numbers?

A: Yes, you can simplify an expression with complex numbers. However, you need to follow the same rules as before: combine like terms and simplify the expression.