Which irrational number is between √14 and √18

Question

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Answer 1

To find an irrational number between \( \sqrt{14} \) and \( \sqrt{18} \), we first calculate the approximate values of these square roots.

Calculating \( \sqrt{14} \): \[ \sqrt{14} \approx 3.74 \]

Calculating \( \sqrt{18} \): \[ \sqrt{18} \approx 4.24 \]

Now, we need to find an irrational number that lies between these two values. One such number could be \( \sqrt{15} \).

Calculating \( \sqrt{15} \): \[ \sqrt{15} \approx 3.87 \]

Since \( 3.74 < \sqrt{15} < 4.24 \), \( \sqrt{15} \) is indeed between \( \sqrt{14} \) and \( \sqrt{18} \).

Thus, an irrational number between \( \sqrt{14} \) and \( \sqrt{18} \) is: \[ \sqrt{15} \]