Find the mean proportional of 6.5 and 24.
\(2\sqrt{39}\)
The mean proportional of two positive numbers \(a\) and \(b\) is \(\sqrt{ab}\).
Here \(a = 6.5\) and \(b = 24\), so the mean proportional is \(\sqrt{6.5 \times 24} = \sqrt{156}\).
Factorise inside the root: \(156 = 4 \times 39\), so \(\sqrt{156} = \sqrt{4 \times 39} = 2\sqrt{39}\).
Hence, the mean proportional of 6.5 and 24 is \(2\sqrt{39}\).
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Important Questions from Mean Proportional
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The mean proportional between 0.16 and 0.64 is:
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