Between Which Two Consecutive Integers Does 138 \sqrt{138} 138 Lie?
Introduction
Mathematics is a vast and fascinating subject that encompasses various branches, including algebra, geometry, and calculus. One of the fundamental concepts in mathematics is the study of numbers, particularly integers and their properties. In this article, we will delve into the world of integers and explore the concept of consecutive integers. We will also examine the problem of finding the two consecutive integers between which the square root of 138 lies.
What are Consecutive Integers?
Consecutive integers are integers that follow each other in order, with no gaps in between. For example, the consecutive integers 3, 4, and 5 are integers that follow each other in order. Consecutive integers can be positive, negative, or zero. In this article, we will focus on finding the two consecutive integers between which the square root of 138 lies.
The Square Root of 138
The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we are interested in finding the square root of 138. To do this, we can use a calculator or a mathematical formula to find the square root of 138.
Finding the Square Root of 138
Using a calculator, we can find that the square root of 138 is approximately 11.73. This means that the square root of 138 lies between the integers 11 and 12.
Why Does the Square Root of 138 Lie Between 11 and 12?
The square root of 138 lies between 11 and 12 because 11 squared (11^2) is 121, which is less than 138. On the other hand, 12 squared (12^2) is 144, which is greater than 138. Therefore, the square root of 138 must lie between 11 and 12.
How to Find the Two Consecutive Integers Between Which the Square Root of 138 Lies
To find the two consecutive integers between which the square root of 138 lies, we can use the following steps:
- Find the square root of 138 using a calculator or a mathematical formula.
- Determine the two integers between which the square root of 138 lies.
- Check if the square of the lower integer is less than 138 and if the square of the higher integer is greater than 138.
Example
Let's use an example to illustrate the concept. Suppose we want to find the two consecutive integers between which the square root of 25 lies. Using a calculator, we can find that the square root of 25 is 5. Therefore, the two consecutive integers between which the square root of 25 lies are 4 and 5.
Conclusion
In conclusion, the square root of 138 lies between the integers 11 and 12. To find the two consecutive integers between which the square root of 138 lies, we can use the steps outlined above. By following these steps, we can determine the two consecutive integers between which the square root of any number lies.
Frequently Asked Questions
- Q: What are consecutive integers? A: Consecutive integers are integers that follow each other in order, with no gaps in between.
- Q: How do I find the two consecutive integers between which the square root of a number lies? A: To find the two consecutive integers between which the square root of a number lies, you can use the steps outlined above.
- Q: Why does the square root of 138 lie between 11 and 12? A: The square root of 138 lies between 11 and 12 because 11 squared (11^2) is 121, which is less than 138. On the other hand, 12 squared (12^2) is 144, which is greater than 138.
Final Thoughts
In this article, we have explored the concept of consecutive integers and how to find the two consecutive integers between which the square root of a number lies. We have also examined the problem of finding the two consecutive integers between which the square root of 138 lies. By following the steps outlined above, we can determine the two consecutive integers between which the square root of any number lies.
References
Introduction
In our previous article, we explored the concept of consecutive integers and how to find the two consecutive integers between which the square root of a number lies. We also examined the problem of finding the two consecutive integers between which the square root of 138 lies. In this article, we will answer some frequently asked questions related to this topic.
Q: What are consecutive integers?
A: Consecutive integers are integers that follow each other in order, with no gaps in between. For example, the consecutive integers 3, 4, and 5 are integers that follow each other in order.
Q: How do I find the two consecutive integers between which the square root of a number lies?
A: To find the two consecutive integers between which the square root of a number lies, you can use the following steps:
- Find the square root of the number using a calculator or a mathematical formula.
- Determine the two integers between which the square root of the number lies.
- Check if the square of the lower integer is less than the number and if the square of the higher integer is greater than the number.
Q: Why does the square root of 138 lie between 11 and 12?
A: The square root of 138 lies between 11 and 12 because 11 squared (11^2) is 121, which is less than 138. On the other hand, 12 squared (12^2) is 144, which is greater than 138.
Q: Can I use a calculator to find the two consecutive integers between which the square root of a number lies?
A: Yes, you can use a calculator to find the two consecutive integers between which the square root of a number lies. Simply enter the number into the calculator and find its square root. Then, determine the two integers between which the square root of the number lies.
Q: What if the square root of a number lies between two non-consecutive integers?
A: If the square root of a number lies between two non-consecutive integers, you can use the following steps to find the two consecutive integers between which the square root of the number lies:
- Find the square root of the number using a calculator or a mathematical formula.
- Determine the two integers between which the square root of the number lies.
- Check if the square of the lower integer is less than the number and if the square of the higher integer is greater than the number.
- If the square of the lower integer is less than the number and the square of the higher integer is greater than the number, then the square root of the number lies between the two integers.
Q: Can I use a mathematical formula to find the two consecutive integers between which the square root of a number lies?
A: Yes, you can use a mathematical formula to find the two consecutive integers between which the square root of a number lies. One such formula is:
√n = √(m^2 + k)
where n is the number, m is the lower integer, and k is the difference between the square of the higher integer and the number.
Q: What if I am unsure about the two consecutive integers between which the square root of a number lies?
A: If you are unsure about the two consecutive integers between which the square root of a number lies, you can use the following steps to find the correct answer:
- Find the square root of the number using a calculator or a mathematical formula.
- Determine the two integers between which the square root of the number lies.
- Check if the square of the lower integer is less than the number and if the square of the higher integer is greater than the number.
- If the square of the lower integer is less than the number and the square of the higher integer is greater than the number, then the square root of the number lies between the two integers.
Conclusion
In conclusion, finding the two consecutive integers between which the square root of a number lies is a simple process that can be done using a calculator or a mathematical formula. By following the steps outlined above, you can determine the two consecutive integers between which the square root of any number lies.
Frequently Asked Questions
- Q: What are consecutive integers? A: Consecutive integers are integers that follow each other in order, with no gaps in between.
- Q: How do I find the two consecutive integers between which the square root of a number lies? A: To find the two consecutive integers between which the square root of a number lies, you can use the steps outlined above.
- Q: Why does the square root of 138 lie between 11 and 12? A: The square root of 138 lies between 11 and 12 because 11 squared (11^2) is 121, which is less than 138. On the other hand, 12 squared (12^2) is 144, which is greater than 138.
Final Thoughts
In this article, we have answered some frequently asked questions related to finding the two consecutive integers between which the square root of a number lies. By following the steps outlined above, you can determine the two consecutive integers between which the square root of any number lies.