Find the mean proportional between 18 and 72.

The correct answer is Option (1) → 36

The mean proportional between \(a\) and \(b\) is the number \(x\) for which \(a:x=x:b\), so \(x^2=ab\) and \(x=\sqrt{ab}\).

• From \(18:x=x:72\), the product of the means equals the product of the extremes: \(x^2=18\times72=1296\)

• \(x=\sqrt{1296}=36\)