Answer :
Sure! Let's find the best estimate for [tex]\(\sqrt{120}\)[/tex] by comparing it with the given options.
We need to find which of the given options is closest to the actual value of [tex]\(\sqrt{120}\)[/tex].
The given options are:
a) 10.1
b) 10.5
c) 10.6
d) 10.9
From the information provided, the value of [tex]\(\sqrt{120}\)[/tex] is approximately 10.954. Now, let's compare this value with each of the given options to see which is the closest.
1. Option a) 10.1:
- Difference: [tex]\( \left| 10.954 - 10.1 \right| = 0.854 \)[/tex]
2. Option b) 10.5:
- Difference: [tex]\( \left| 10.954 - 10.5 \right| = 0.454 \)[/tex]
3. Option c) 10.6:
- Difference: [tex]\( \left| 10.954 - 10.6 \right| = 0.354 \)[/tex]
4. Option d) 10.9:
- Difference: [tex]\( \left| 10.954 - 10.9 \right| = 0.054 \)[/tex]
We can see that the smallest difference is with option d) 10.9.
Therefore, the best estimate for [tex]\(\sqrt{120}\)[/tex] is:
d) 10.9
We need to find which of the given options is closest to the actual value of [tex]\(\sqrt{120}\)[/tex].
The given options are:
a) 10.1
b) 10.5
c) 10.6
d) 10.9
From the information provided, the value of [tex]\(\sqrt{120}\)[/tex] is approximately 10.954. Now, let's compare this value with each of the given options to see which is the closest.
1. Option a) 10.1:
- Difference: [tex]\( \left| 10.954 - 10.1 \right| = 0.854 \)[/tex]
2. Option b) 10.5:
- Difference: [tex]\( \left| 10.954 - 10.5 \right| = 0.454 \)[/tex]
3. Option c) 10.6:
- Difference: [tex]\( \left| 10.954 - 10.6 \right| = 0.354 \)[/tex]
4. Option d) 10.9:
- Difference: [tex]\( \left| 10.954 - 10.9 \right| = 0.054 \)[/tex]
We can see that the smallest difference is with option d) 10.9.
Therefore, the best estimate for [tex]\(\sqrt{120}\)[/tex] is:
d) 10.9
