Answer :
To find the number that is closest to [tex]\(\sqrt{114}\)[/tex], we begin by estimating the square root of 114.
The approximate square root of 114 is 10.68. Now, we need to check which of the given numbers is closest to this value. The options provided are 10.1, 10.6, 11.1, and 9.9.
Let's find the absolute difference between each option and 10.68:
1. Calculate the difference between 10.1 and 10.68:
- Difference: [tex]\(|10.1 - 10.68| = 0.58\)[/tex]
2. Calculate the difference between 10.6 and 10.68:
- Difference: [tex]\(|10.6 - 10.68| = 0.08\)[/tex]
3. Calculate the difference between 11.1 and 10.68:
- Difference: [tex]\(|11.1 - 10.68| = 0.42\)[/tex]
4. Calculate the difference between 9.9 and 10.68:
- Difference: [tex]\(|9.9 - 10.68| = 0.78\)[/tex]
Next, we compare all these differences to determine which is the smallest:
- The difference for 10.1 is 0.58.
- The difference for 10.6 is 0.08.
- The difference for 11.1 is 0.42.
- The difference for 9.9 is 0.78.
The smallest difference is 0.08, which corresponds to 10.6.
Therefore, the number closest to [tex]\(\sqrt{114}\)[/tex] is 10.6.
The approximate square root of 114 is 10.68. Now, we need to check which of the given numbers is closest to this value. The options provided are 10.1, 10.6, 11.1, and 9.9.
Let's find the absolute difference between each option and 10.68:
1. Calculate the difference between 10.1 and 10.68:
- Difference: [tex]\(|10.1 - 10.68| = 0.58\)[/tex]
2. Calculate the difference between 10.6 and 10.68:
- Difference: [tex]\(|10.6 - 10.68| = 0.08\)[/tex]
3. Calculate the difference between 11.1 and 10.68:
- Difference: [tex]\(|11.1 - 10.68| = 0.42\)[/tex]
4. Calculate the difference between 9.9 and 10.68:
- Difference: [tex]\(|9.9 - 10.68| = 0.78\)[/tex]
Next, we compare all these differences to determine which is the smallest:
- The difference for 10.1 is 0.58.
- The difference for 10.6 is 0.08.
- The difference for 11.1 is 0.42.
- The difference for 9.9 is 0.78.
The smallest difference is 0.08, which corresponds to 10.6.
Therefore, the number closest to [tex]\(\sqrt{114}\)[/tex] is 10.6.
