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

Question

Responses

13−−√
start root 13 end root

15−−√
start root 15 end root

10−−√
start root 10 end root

19−−√

Answer 1

To determine which irrational number is between \(\sqrt{14}\) and \(\sqrt{18}\), we can first calculate the approximate decimal values of \(\sqrt{14}\) and \(\sqrt{18}\):

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

Next, we'll find the approximate values of the options provided:

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

Now we can compare:

• \(\sqrt{14} \approx 3.74 < \sqrt{15} \approx 3.87 < \sqrt{18} \approx 4.24\)

From this, we see that \(\sqrt{15}\) falls between \(\sqrt{14}\) and \(\sqrt{18}\).

Thus, the irrational number between \(\sqrt{14}\) and \(\sqrt{18}\) is:

\(\sqrt{15}\)