Evaluate The Expression:$\[ B = \sqrt{6 - 2 \sqrt{8}} \\]

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Introduction

In this article, we will delve into the world of mathematics and evaluate the given expression $B = \sqrt{6 - 2 \sqrt{8}}$. This expression involves square roots and is a great example of how to simplify complex mathematical expressions. We will break down the expression step by step, using various mathematical techniques to arrive at the final value of $B$.

Understanding the Expression

The given expression is $B = \sqrt{6 - 2 \sqrt{8}}$. To evaluate this expression, we need to start by simplifying the term inside the square root, which is $6 - 2 \sqrt{8}$. We can simplify this term by first evaluating the square root of $8$, which is $\sqrt{8} = \sqrt{4 \cdot 2} = 2 \sqrt{2}$.

Simplifying the Expression

Now that we have simplified the term inside the square root, we can rewrite the expression as $B = \sqrt{6 - 2 \cdot 2 \sqrt{2}}$. We can further simplify this expression by combining the constants inside the square root, which gives us $B = \sqrt{6 - 4 \sqrt{2}}$.

Using the Difference of Squares Formula

The expression $B = \sqrt{6 - 4 \sqrt{2}}$ can be simplified using the difference of squares formula, which states that $a^2 - b^2 = (a + b)(a - b)$. We can rewrite the expression as $B = \sqrt{(2 - \sqrt{2})^2}$.

Evaluating the Expression

Now that we have simplified the expression using the difference of squares formula, we can evaluate it by taking the square root of the term inside the square root. This gives us $B = 2 - \sqrt{2}$.

Conclusion

In this article, we evaluated the expression $B = \sqrt{6 - 2 \sqrt{8}}$ using various mathematical techniques. We simplified the term inside the square root, used the difference of squares formula, and finally arrived at the value of $B = 2 - \sqrt{2}$. This expression is a great example of how to simplify complex mathematical expressions and is a useful tool for anyone studying mathematics.

Final Answer

The final answer to the expression $B = \sqrt{6 - 2 \sqrt{8}}$ is $B = 2 - \sqrt{2}$.

Related Topics

• Simplifying square roots
• Difference of squares formula
• Evaluating mathematical expressions

References

• [1] "Simplifying Square Roots" by Math Open Reference
• [2] "Difference of Squares Formula" by Khan Academy
• [3] "Evaluating Mathematical Expressions" by Wolfram Alpha

Further Reading

• "Simplifying Radical Expressions" by Mathway
• "Evaluating Square Roots" by Purplemath
• "Mathematical Expressions" by MIT OpenCourseWare
  

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Introduction

In our previous article, we evaluated the expression $B = \sqrt{6 - 2 \sqrt{8}}$ using various mathematical techniques. In this article, we will answer some frequently asked questions related to this expression and provide additional insights into the world of mathematics.

Q&A

Q: What is the value of $B$?

A: The value of $B$ is $2 - \sqrt{2}$.

Q: How do I simplify the term inside the square root?

A: To simplify the term inside the square root, you can start by evaluating the square root of $8$, which is $\sqrt{8} = \sqrt{4 \cdot 2} = 2 \sqrt{2}$. Then, you can rewrite the expression as $B = \sqrt{6 - 2 \cdot 2 \sqrt{2}}$ and combine the constants inside the square root.

Q: What is the difference of squares formula?

A: The difference of squares formula is $a^2 - b^2 = (a + b)(a - b)$. This formula can be used to simplify expressions of the form $a^2 - b^2$.

Q: How do I use the difference of squares formula to simplify the expression?

A: To use the difference of squares formula, you can rewrite the expression as $B = \sqrt{(2 - \sqrt{2})^2}$. Then, you can simplify the expression by taking the square root of the term inside the square root.

Q: What is the final answer to the expression?

A: The final answer to the expression $B = \sqrt{6 - 2 \sqrt{8}}$ is $B = 2 - \sqrt{2}$.

Q: What are some related topics to this expression?

A: Some related topics to this expression include simplifying square roots, difference of squares formula, and evaluating mathematical expressions.

Q: Where can I find more information on this topic?

A: You can find more information on this topic by visiting the following resources:

• [1] "Simplifying Square Roots" by Math Open Reference
• [2] "Difference of Squares Formula" by Khan Academy
• [3] "Evaluating Mathematical Expressions" by Wolfram Alpha

Additional Insights

• Simplifying square roots can be a challenging task, but with practice and patience, you can become proficient in simplifying complex expressions.
• The difference of squares formula is a powerful tool for simplifying expressions of the form $a^2 - b^2$.
• Evaluating mathematical expressions requires a deep understanding of mathematical concepts and techniques.

Conclusion

In this article, we answered some frequently asked questions related to the expression $B = \sqrt{6 - 2 \sqrt{8}}$ and provided additional insights into the world of mathematics. We hope that this article has been helpful in clarifying any doubts you may have had about this expression.

Final Answer

The final answer to the expression $B = \sqrt{6 - 2 \sqrt{8}}$ is $B = 2 - \sqrt{2}$.

Related Topics

• Simplifying square roots
• Difference of squares formula
• Evaluating mathematical expressions

References

• [1] "Simplifying Square Roots" by Math Open Reference
• [2] "Difference of Squares Formula" by Khan Academy
• [3] "Evaluating Mathematical Expressions" by Wolfram Alpha

Further Reading

• "Simplifying Radical Expressions" by Mathway
• "Evaluating Square Roots" by Purplemath
• "Mathematical Expressions" by MIT OpenCourseWare