Simplify The Expression:$-6 \sqrt{7} - 6 \sqrt{7}$

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Introduction

When dealing with mathematical expressions, simplifying them is an essential step to understand and work with them effectively. In this article, we will focus on simplifying the given expression: −67−67-6 \sqrt{7} - 6 \sqrt{7}. This expression involves the addition of two terms that contain the square root of 7. Our goal is to simplify this expression by combining like terms and applying the rules of arithmetic operations.

Understanding the Expression

The given expression is −67−67-6 \sqrt{7} - 6 \sqrt{7}. This expression consists of two terms: −67-6 \sqrt{7} and −67-6 \sqrt{7}. Both terms have the same coefficient, which is -6, and the same radical, which is 7\sqrt{7}. When we add these two terms together, we are essentially combining like terms.

Combining Like Terms

To combine like terms, we need to follow the rules of arithmetic operations. When adding or subtracting terms with the same coefficient and radical, we can combine them by adding or subtracting their coefficients. In this case, we have two terms with the same coefficient (-6) and radical (7\sqrt{7}). Therefore, we can combine them by adding their coefficients.

Simplifying the Expression

Now, let's simplify the expression by combining the two terms:

−67−67-6 \sqrt{7} - 6 \sqrt{7}

Using the rule of combining like terms, we can add the coefficients:

(−6+(−6))7(-6 + (-6)) \sqrt{7}

Simplifying the expression inside the parentheses, we get:

−127-12 \sqrt{7}

Therefore, the simplified expression is −127-12 \sqrt{7}.

Conclusion

In this article, we simplified the expression −67−67-6 \sqrt{7} - 6 \sqrt{7} by combining like terms. We followed the rules of arithmetic operations and added the coefficients of the two terms to get the simplified expression. The final answer is −127-12 \sqrt{7}.

Frequently Asked Questions

  • Q: What is the simplified expression of −67−67-6 \sqrt{7} - 6 \sqrt{7}? A: The simplified expression is −127-12 \sqrt{7}.
  • Q: How do we combine like terms in an expression? A: We combine like terms by adding or subtracting their coefficients.
  • Q: What is the rule for combining like terms? A: The rule is to add or subtract the coefficients of the terms with the same radical.

Final Answer

The final answer is −127-12 \sqrt{7}.

Introduction

In our previous article, we simplified the expression −67−67-6 \sqrt{7} - 6 \sqrt{7} by combining like terms. We followed the rules of arithmetic operations and added the coefficients of the two terms to get the simplified expression. In this article, we will provide a Q&A section to address some common questions and doubts related to simplifying expressions.

Q&A

Q: What is the simplified expression of −67−67-6 \sqrt{7} - 6 \sqrt{7}?

A: The simplified expression is −127-12 \sqrt{7}.

Q: How do we combine like terms in an expression?

A: We combine like terms by adding or subtracting their coefficients. For example, in the expression −67−67-6 \sqrt{7} - 6 \sqrt{7}, we can combine the two terms by adding their coefficients: (−6+(−6))7(-6 + (-6)) \sqrt{7}.

Q: What is the rule for combining like terms?

A: The rule is to add or subtract the coefficients of the terms with the same radical. For example, in the expression −67+37-6 \sqrt{7} + 3 \sqrt{7}, we can combine the two terms by adding their coefficients: (−6+3)7(-6 + 3) \sqrt{7}.

Q: Can we simplify an expression with different radicals?

A: No, we cannot simplify an expression with different radicals. For example, in the expression −67+32-6 \sqrt{7} + 3 \sqrt{2}, we cannot combine the two terms because they have different radicals.

Q: How do we simplify an expression with a negative coefficient?

A: We simplify an expression with a negative coefficient by following the same rules as before. For example, in the expression −67−67-6 \sqrt{7} - 6 \sqrt{7}, we can combine the two terms by adding their coefficients: (−6+(−6))7(-6 + (-6)) \sqrt{7}.

Q: Can we simplify an expression with a variable in the radical?

A: No, we cannot simplify an expression with a variable in the radical. For example, in the expression −6x−6x-6 \sqrt{x} - 6 \sqrt{x}, we cannot combine the two terms because they have a variable in the radical.

Q: How do we simplify an expression with a coefficient in the radical?

A: We simplify an expression with a coefficient in the radical by following the same rules as before. For example, in the expression −67−67-6 \sqrt{7} - 6 \sqrt{7}, we can combine the two terms by adding their coefficients: (−6+(−6))7(-6 + (-6)) \sqrt{7}.

Conclusion

In this article, we provided a Q&A section to address some common questions and doubts related to simplifying expressions. We covered topics such as combining like terms, rules for combining like terms, and simplifying expressions with different radicals, negative coefficients, variables in the radical, and coefficients in the radical.

Final Answer

The final answer is −127-12 \sqrt{7}.

Additional Resources

Related Articles

Tags

  • Simplifying expressions
  • Combining like terms
  • Rules for combining like terms
  • Negative coefficients
  • Variables in the radical
  • Coefficients in the radical

Categories

  • Mathematics
  • Algebra
  • Simplifying expressions
  • Combining like terms
  • Rules for combining like terms