Which irrational number is between 14−−√

and 18−−√
?(1 point)
Responses

10−−√
start root 10 end root

13−−√
start root 13 end root

19−−√
start root 19 end root

15−−√

1 answer

To find an irrational number between \(\sqrt{14}\) and \(\sqrt{18}\), we can first determine approximate decimal values for \(\sqrt{14}\) and \(\sqrt{18}\).

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

Now, we need to evaluate the options provided:

  • \(\sqrt{10} \approx 3.16\)
  • \(\sqrt{13} \approx 3.61\)
  • \(\sqrt{19} \approx 4.36\)
  • \(\sqrt{15} \approx 3.87\)

To find a number between \(\sqrt{14}\) and \(\sqrt{18}\) (approximately between 3.74 and 4.24):

  • \(\sqrt{10} \approx 3.16\) (too low)
  • \(\sqrt{13} \approx 3.61\) (too low)
  • \(\sqrt{19} \approx 4.36\) (too high)
  • \(\sqrt{15} \approx 3.87\) (within range)

The number that is between \(\sqrt{14}\) and \(\sqrt{18}\) is \(\sqrt{15}\).

Thus, the answer is:

\(\sqrt{15}\)