To determine which of the given points most closely represents the square root of 97, we need to first find the numerical value of [tex]\(\sqrt{97}\)[/tex].
The square root of 97 is approximately:
[tex]\[ \sqrt{97} \approx 9.848857801796104 \][/tex]
Next, we compare this value to the provided choices:
- 9.9
- 10
- 9.5
- 9.6
- 9.7
- 9.8
We need to find which of these values is closest to 9.848857801796104. To do this, we calculate the absolute difference between each of the choices and the value 9.848857801796104:
- The difference between 9.9 and 9.848857801796104 is approximately 0.05114219820389643.
- The difference between 10 and 9.848857801796104 is approximately 0.15114219820389607.
- The difference between 9.5 and 9.848857801796104 is approximately 0.34885780179610393.
- The difference between 9.6 and 9.848857801796104 is approximately 0.24885780179610428.
- The difference between 9.7 and 9.848857801796104 is approximately 0.14885780179610464.
- The difference between 9.8 and 9.848857801796104 is approximately 0.04885780179610322.
We see that the smallest difference is between 9.8 and 9.848857801796104, which is approximately 0.04885780179610322. Therefore, the point that most closely represents [tex]\(\sqrt{97}\)[/tex] is:
9.8
