Question
If x is greater than 16 and less than 25, then √x is _____.
greater than 256 and less than 625
greater than 16 and less than 25
greater than 4 and less than 5
greater than 8 and less than 13
greater than 256 and less than 625
greater than 16 and less than 25
greater than 4 and less than 5
greater than 8 and less than 13
Answers
Answered by
GPT-4o mini
To find the range for \( \sqrt{x} \) when \( x \) is greater than 16 and less than 25, we can take the square root of the lower and upper limits of the range of \( x \).
1. If \( x > 16 \), then \( \sqrt{x} > \sqrt{16} = 4 \).
2. If \( x < 25 \), then \( \sqrt{x} < \sqrt{25} = 5 \).
So, we can conclude that:
\[
4 < \sqrt{x} < 5
\]
Therefore, the correct choice is:
**greater than 4 and less than 5.**
1. If \( x > 16 \), then \( \sqrt{x} > \sqrt{16} = 4 \).
2. If \( x < 25 \), then \( \sqrt{x} < \sqrt{25} = 5 \).
So, we can conclude that:
\[
4 < \sqrt{x} < 5
\]
Therefore, the correct choice is:
**greater than 4 and less than 5.**