Question
A whole number square root lies between 10 and 11 but is closer to 11. Identify the whole number square root that satisfies this requirement.(1 point)
Responses
110−−−√
Start Root 110 End Root
111−−−√
Start Root 111 End Root
101−−−√
Start Root 101 End Root
108−−−√
Responses
110−−−√
Start Root 110 End Root
111−−−√
Start Root 111 End Root
101−−−√
Start Root 101 End Root
108−−−√
Answers
GPT-4o mini
To find the whole number square root that lies between 10 and 11 but is closer to 11, we first note the squares of 10 and 11:
- \(10^2 = 100\)
- \(11^2 = 121\)
This means any number whose square root is between 10 and 11 will fall between 100 and 121.
Now, we need to check the numbers given in the responses to find which one is closer to 121 (the square of 11), but still less than 121:
1. \(\sqrt{110} \approx 10.488\)
2. \(\sqrt{111} \approx 10.535\)
3. \(\sqrt{101} \approx 10.05\)
4. \(\sqrt{108} \approx 10.392\)
Among these, \(\sqrt{111} \approx 10.535\) is the closest to 11 while still being between 10 and 11.
Therefore, the correct response is:
\(\sqrt{111}\)
- \(10^2 = 100\)
- \(11^2 = 121\)
This means any number whose square root is between 10 and 11 will fall between 100 and 121.
Now, we need to check the numbers given in the responses to find which one is closer to 121 (the square of 11), but still less than 121:
1. \(\sqrt{110} \approx 10.488\)
2. \(\sqrt{111} \approx 10.535\)
3. \(\sqrt{101} \approx 10.05\)
4. \(\sqrt{108} \approx 10.392\)
Among these, \(\sqrt{111} \approx 10.535\) is the closest to 11 while still being between 10 and 11.
Therefore, the correct response is:
\(\sqrt{111}\)