Simplify { \frac 9}{\sqrt{7}}$}$.The Result Can Be Expressed In The Form { \frac{A}{B}$}$ Where { A = \square$ ${ B = \square\$} Entry Tip: Do Not Use A Decimal Approximation For Square Roots. Preview Your Answer
Introduction
In this article, we will simplify the given expression {\frac{9}{\sqrt{7}}$}$ and express it in the form {\frac{A}{B}$}$ where {A = \square$}$ and {B = \square$}$. We will use mathematical techniques to simplify the expression and provide the final result.
Understanding the Expression
The given expression is {\frac{9}{\sqrt{7}}$}$. This expression can be simplified by rationalizing the denominator, which involves multiplying the numerator and denominator by the conjugate of the denominator.
Rationalizing the Denominator
To rationalize the denominator, we need to multiply the numerator and denominator by the conjugate of the denominator. The conjugate of {\sqrt{7}$}$ is {\sqrt{7}$}$ itself. Therefore, we multiply the numerator and denominator by {\sqrt{7}$}$.
{\frac{9}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{9\sqrt{7}}{7}$}$
Simplifying the Expression
The expression {\frac{9\sqrt{7}}{7}$}$ is already in the form {\frac{A}{B}$}$ where {A = 9\sqrt{7}$}$ and {B = 7$}$. Therefore, the simplified expression is {\frac{9\sqrt{7}}{7}$}$.
Conclusion
In this article, we simplified the given expression {\frac{9}{\sqrt{7}}$}$ and expressed it in the form {\frac{A}{B}$}$ where {A = 9\sqrt{7}$}$ and {B = 7$}$. We used mathematical techniques to rationalize the denominator and simplify the expression.
Final Answer
The final answer is {\frac{9\sqrt{7}}{7}$}$.
Additional Information
- The expression {\frac{9}{\sqrt{7}}$}$ can be simplified by rationalizing the denominator.
- The conjugate of {\sqrt{7}$}$ is {\sqrt{7}$}$ itself.
- The expression {\frac{9\sqrt{7}}{7}$}$ is already in the form {\frac{A}{B}$}$ where {A = 9\sqrt{7}$}$ and {B = 7$}$.
Related Topics
- Rationalizing the denominator
- Simplifying expressions
- Conjugate of a square root
References
Frequently Asked Questions
- Q: How do I simplify the expression {\frac{9}{\sqrt{7}}$}$?
- A: You can simplify the expression by rationalizing the denominator.
- Q: What is the conjugate of {\sqrt{7}$}$?
- A: The conjugate of {\sqrt{7}$}$ is {\sqrt{7}$}$ itself.
Simplify {\frac{9}{\sqrt{7}}$}$ Q&A =====================================
Introduction
In this article, we will provide a Q&A section to help you understand the concept of simplifying the expression {\frac{9}{\sqrt{7}}$}$. We will cover various questions and answers related to rationalizing the denominator, simplifying expressions, and conjugate of a square root.
Q&A
Q: What is the concept of rationalizing the denominator?
A: Rationalizing the denominator is a mathematical technique used to simplify an expression by eliminating the square root from the denominator.
Q: How do I rationalize the denominator of the expression {\frac{9}{\sqrt{7}}$}$?
A: To rationalize the denominator, you need to multiply the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of {\sqrt{7}$}$ is {\sqrt{7}$}$ itself.
Q: What is the conjugate of {\sqrt{7}$}$?
A: The conjugate of {\sqrt{7}$}$ is {\sqrt{7}$}$ itself.
Q: How do I simplify the expression {\frac{9}{\sqrt{7}}$}$?
A: You can simplify the expression by rationalizing the denominator. Multiply the numerator and denominator by the conjugate of the denominator, which is {\sqrt{7}$}$ itself.
Q: What is the final answer to the expression {\frac{9}{\sqrt{7}}$}$?
A: The final answer is {\frac{9\sqrt{7}}{7}$}$.
Q: Can I use a decimal approximation for square roots?
A: No, you should not use a decimal approximation for square roots. Instead, use the exact value of the square root.
Q: What are some common mistakes to avoid when simplifying expressions?
A: Some common mistakes to avoid include:
- Not rationalizing the denominator
- Not using the exact value of the square root
- Not following the order of operations
Q: How do I check my answer for the expression {\frac{9}{\sqrt{7}}$}$?
A: To check your answer, multiply the numerator and denominator by the conjugate of the denominator and simplify the expression.
Conclusion
In this article, we provided a Q&A section to help you understand the concept of simplifying the expression {\frac{9}{\sqrt{7}}$}$. We covered various questions and answers related to rationalizing the denominator, simplifying expressions, and conjugate of a square root.
Final Answer
The final answer is {\frac{9\sqrt{7}}{7}$}$.
Additional Information
- The expression {\frac{9}{\sqrt{7}}$}$ can be simplified by rationalizing the denominator.
- The conjugate of {\sqrt{7}$}$ is {\sqrt{7}$}$ itself.
- The expression {\frac{9\sqrt{7}}{7}$}$ is already in the form {\frac{A}{B}$}$ where {A = 9\sqrt{7}$}$ and {B = 7$}$.
Related Topics
- Rationalizing the denominator
- Simplifying expressions
- Conjugate of a square root
References
Frequently Asked Questions
- Q: How do I simplify the expression {\frac{9}{\sqrt{7}}$}$?
- A: You can simplify the expression by rationalizing the denominator.
- Q: What is the conjugate of {\sqrt{7}$}$?
- A: The conjugate of {\sqrt{7}$}$ is {\sqrt{7}$}$ itself.