The square root of 121 is 11

Oct 13, 2025 by leolavanderia.com.br 67 views

Understanding the Problem

When evaluating the expression $-\sqrt{121}$ , we need to consider the properties of square roots and the effect of the negative sign. Square roots are the inverse operation of squaring a number, and they return a value that, when multiplied by itself, gives the original number. In this case, we are dealing with the square root of 121.

Properties of Square Roots

The square root of a number can be either positive or negative, and both values satisfy the equation. For example, the square root of 16 is both 4 and -4, since both 4^2 and (-4)^2 equal 16. However, when we see a square root symbol, we usually assume the positive value. In this case, we have $-\sqrt{121}$ , which means we are looking for the negative value of the square root of 121.

Evaluating the Expression

To evaluate the expression $-\sqrt{121}$ , we need to find the square root of 121 first. The square root of 121 is 11, since 11^2 equals 121. Now, we need to apply the negative sign to the result. When we multiply a number by -1, we change its sign. Therefore, the negative of 11 is -11.

Conclusion

In conclusion, the value of $-\sqrt{121}$ is -11. This is because the square root of 121 is 11, and applying the negative sign to 11 gives us -11.

Real-World Applications

Understanding how to evaluate expressions with negative square roots is crucial in various real-world applications, such as:

Physics and Engineering: When dealing with distances, velocities, and accelerations, we often encounter square roots. In these cases, it's essential to consider both the positive and negative values of the square root.
Computer Science: In computer programming, we frequently encounter mathematical operations, including square roots. Understanding how to evaluate expressions with negative square roots is vital in developing accurate algorithms.
Finance: In finance, we often work with square roots when calculating interest rates, stock prices, and other financial metrics. Accurate evaluation of expressions with negative square roots is critical in making informed investment decisions.

Tips and Tricks

When evaluating expressions with negative square roots, remember to:

Always consider both the positive and negative values of the square root.
Apply the negative sign to the result of the square root.
Use the correct order of operations to evaluate the expression.

Common Mistakes

When evaluating expressions with negative square roots, be aware of the following common mistakes:

Forgetting to consider the negative value of the square root.
Applying the negative sign incorrectly.
Not following the correct order of operations.

Final Thoughts

Evaluating expressions with negative square roots requires a solid understanding of the properties of square roots and the effect of the negative sign. By following the correct procedures and avoiding common mistakes, you can accurately evaluate expressions like $-\sqrt{121}$ and apply this knowledge in various real-world applications.

Frequently Asked Questions

Q: What is the difference between a positive and negative square root?

A: The square root of a number can be either positive or negative, and both values satisfy the equation. For example, the square root of 16 is both 4 and -4, since both 4^2 and (-4)^2 equal 16.

Q: How do I evaluate an expression with a negative square root?

A: To evaluate an expression with a negative square root, you need to find the square root of the number first, and then apply the negative sign to the result. For example, to evaluate $-\sqrt{121}$ , you would first find the square root of 121, which is 11, and then apply the negative sign to get -11.

Q: What is the order of operations when evaluating an expression with a negative square root?

A: When evaluating an expression with a negative square root, you need to follow the correct order of operations:

Evaluate the expression inside the square root.
Find the square root of the result.
Apply the negative sign to the result.

Q: Can I simplify an expression with a negative square root?

A: Yes, you can simplify an expression with a negative square root by combining the negative sign with the square root. For example, $-\sqrt{121}$ can be simplified to -11.

Q: How do I handle expressions with multiple negative signs?

A: When handling expressions with multiple negative signs, you need to follow the correct order of operations and apply the negative signs correctly. For example, to evaluate $-(-\sqrt{121})$ , you would first simplify the expression inside the parentheses, which is -11, and then apply the negative sign to get 11.

Q: What are some common mistakes to avoid when evaluating expressions with negative square roots?

A: Some common mistakes to avoid when evaluating expressions with negative square roots include:

Forgetting to consider the negative value of the square root.
Applying the negative sign incorrectly.
Not following the correct order of operations.

Q: How do I apply this knowledge in real-world applications?

A: Understanding how to evaluate expressions with negative square roots is crucial in various real-world applications, such as:

Physics and Engineering: When dealing with distances, velocities, and accelerations, we often encounter square roots. In these cases, it's essential to consider both the positive and negative values of the square root.
Computer Science: In computer programming, we frequently encounter mathematical operations, including square roots. Understanding how to evaluate expressions with negative square roots is vital in developing accurate algorithms.
Finance: In finance, we often work with square roots when calculating interest rates, stock prices, and other financial metrics. Accurate evaluation of expressions with negative square roots is critical in making informed investment decisions.

Q: What are some tips for mastering expressions with negative square roots?

A: Some tips for mastering expressions with negative square roots include:

Always consider both the positive and negative values of the square root.
Apply the negative sign correctly.
Use the correct order of operations to evaluate the expression.
Practice, practice, practice!