Choose The TRUE Statement About 165 \sqrt{165} 165 ​ .A. It Lies Between 8 And 9 On A Number Line.B. It Lies Between 11 And 12 On A Number Line.C. It Lies Between 12 And 13 On A Number Line.D. It Lies Between 13 And 14 On A Number Line.

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In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. In this article, we will explore the square root of 165 and determine which of the given options is the true statement.

What is the Square Root of 165?

The square root of 165 is a mathematical operation that involves finding a value that, when multiplied by itself, gives 165. To find the square root of 165, we can use various methods, including the use of a calculator or the long division method.

Using a Calculator to Find the Square Root of 165

One of the easiest ways to find the square root of 165 is by using a calculator. By entering the number 165 into a calculator and pressing the square root button, we can quickly determine the value of the square root of 165.

The Square Root of 165 is Approximately 12.806

Using a calculator, we find that the square root of 165 is approximately 12.806. This value is a decimal approximation of the square root of 165.

Evaluating the Options

Now that we know the square root of 165 is approximately 12.806, we can evaluate the given options to determine which one is the true statement.

Option A: It lies between 8 and 9 on a number line.

This option is incorrect because the square root of 165 is approximately 12.806, which is greater than 9.

Option B: It lies between 11 and 12 on a number line.

This option is correct because the square root of 165 is approximately 12.806, which lies between 11 and 12 on a number line.

Option C: It lies between 12 and 13 on a number line.

This option is incorrect because the square root of 165 is approximately 12.806, which is less than 13.

Option D: It lies between 13 and 14 on a number line.

This option is incorrect because the square root of 165 is approximately 12.806, which is less than 14.

Conclusion

In conclusion, the true statement about the square root of 165 is that it lies between 11 and 12 on a number line. This is because the square root of 165 is approximately 12.806, which falls within this range.

Why is Understanding the Square Root of 165 Important?

Understanding the square root of 165 is important in various mathematical and real-world applications. For example, in geometry, the square root of 165 can be used to find the length of the sides of a square or rectangle. In physics, the square root of 165 can be used to calculate the energy of a particle.

Real-World Applications of the Square Root of 165

The square root of 165 has various real-world applications, including:

  • Geometry: The square root of 165 can be used to find the length of the sides of a square or rectangle.
  • Physics: The square root of 165 can be used to calculate the energy of a particle.
  • Engineering: The square root of 165 can be used to design and optimize systems, such as bridges and buildings.
  • Computer Science: The square root of 165 can be used in algorithms and data structures, such as binary search trees.

Final Thoughts

In this article, we will answer some of the most frequently asked questions about the square root of 165.

Q: What is the square root of 165?

A: The square root of 165 is a mathematical operation that involves finding a value that, when multiplied by itself, gives 165. The square root of 165 is approximately 12.806.

Q: How do I find the square root of 165?

A: There are several ways to find the square root of 165, including:

  • Using a calculator: Simply enter the number 165 into a calculator and press the square root button.
  • Long division method: This method involves dividing 165 by a series of numbers to find the square root.
  • Estimation method: This method involves estimating the square root of 165 by finding the square root of a nearby perfect square.

Q: What is the significance of the square root of 165?

A: The square root of 165 has various real-world applications, including:

  • Geometry: The square root of 165 can be used to find the length of the sides of a square or rectangle.
  • Physics: The square root of 165 can be used to calculate the energy of a particle.
  • Engineering: The square root of 165 can be used to design and optimize systems, such as bridges and buildings.
  • Computer Science: The square root of 165 can be used in algorithms and data structures, such as binary search trees.

Q: Can I use the square root of 165 in real-world applications?

A: Yes, the square root of 165 can be used in various real-world applications, including:

  • Building design: The square root of 165 can be used to design and optimize buildings, such as bridges and skyscrapers.
  • Engineering: The square root of 165 can be used to design and optimize systems, such as power plants and water treatment plants.
  • Computer Science: The square root of 165 can be used in algorithms and data structures, such as binary search trees.

Q: How do I calculate the square root of 165 using a calculator?

A: To calculate the square root of 165 using a calculator, follow these steps:

  1. Enter the number 165 into the calculator.
  2. Press the square root button.
  3. The calculator will display the square root of 165, which is approximately 12.806.

Q: Can I use the square root of 165 in mathematical equations?

A: Yes, the square root of 165 can be used in mathematical equations, including:

  • Algebra: The square root of 165 can be used to solve equations involving square roots.
  • Geometry: The square root of 165 can be used to find the length of the sides of a square or rectangle.
  • Trigonometry: The square root of 165 can be used to solve equations involving trigonometric functions.

Q: What are some common mistakes to avoid when working with the square root of 165?

A: Some common mistakes to avoid when working with the square root of 165 include:

  • Not using the correct calculator settings.
  • Not checking the calculator for errors.
  • Not using the correct mathematical operations.
  • Not checking the units of measurement.

Conclusion

In conclusion, the square root of 165 is an important mathematical concept that has various real-world applications. By understanding the square root of 165, we can solve problems in geometry, physics, engineering, and computer science.