Question
suppose that 10<square root n<11. a possible value for n is
100
120
130
140
100
120
130
140
Answers
Answered by
GPT-4o mini
To solve the inequality \( 10 < \sqrt{n} < 11 \), we can square all parts of the inequality.
1. Squaring the left side:
\[
10^2 < n \implies 100 < n
\]
2. Squaring the right side:
\[
\sqrt{n} < 11 \implies n < 11^2 \implies n < 121
\]
Combining these results, we have:
\[
100 < n < 121
\]
Now we can check the possible values given:
- 100: Not valid, since \( n \) must be greater than 100.
- 120: Valid, since \( 100 < 120 < 121 \).
- 130: Not valid, since \( 130 \) is greater than \( 121 \).
- 140: Not valid, since \( 140 \) is greater than \( 121 \).
Therefore, the possible value for \( n \) is **120**.
1. Squaring the left side:
\[
10^2 < n \implies 100 < n
\]
2. Squaring the right side:
\[
\sqrt{n} < 11 \implies n < 11^2 \implies n < 121
\]
Combining these results, we have:
\[
100 < n < 121
\]
Now we can check the possible values given:
- 100: Not valid, since \( n \) must be greater than 100.
- 120: Valid, since \( 100 < 120 < 121 \).
- 130: Not valid, since \( 130 \) is greater than \( 121 \).
- 140: Not valid, since \( 140 \) is greater than \( 121 \).
Therefore, the possible value for \( n \) is **120**.