Which irrational number is between 14−−√ and 18−−√?(1 point)

Question

Responses

19−−√
start root 19 end root

13−−√
start root 13 end root

15−−√
start root 15 end root

10−−√

Answer 1

To find which of the given irrational numbers is between \( \sqrt{14} \) and \( \sqrt{18} \), we first evaluate the approximate values of \( \sqrt{14} \) and \( \sqrt{18} \):

• \( \sqrt{14} \approx 3.74 \)
• \( \sqrt{18} \approx 4.24 \)

Now, we can approximate the values of the given options:

1. \( \sqrt{19} \approx 4.36 \)
2. \( \sqrt{13} \approx 3.61 \)
3. \( \sqrt{15} \approx 3.87 \)
4. \( \sqrt{10} \approx 3.16 \)

Now, we see if any of these values fall between \( \sqrt{14} \) and \( \sqrt{18} \):

• \( \sqrt{19} \approx 4.36 \) (not between)
• \( \sqrt{13} \approx 3.61 \) (not between)
• \( \sqrt{15} \approx 3.87 \) (between)
• \( \sqrt{10} \approx 3.16 \) (not between)

So, the irrational number that is between \( \sqrt{14} \) and \( \sqrt{18} \) is \( \sqrt{15} \).