Find the mean proportional between
$(1) 6$ and $24$ , $(2) 360 a^{4}$ and $250 a^{2} b^{2}$ .

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Solution

For two numbers $a, c$ the mean proportional $b$ is
$b = \sqrt{a c}$

So for the first part we have, mean proportional

$= \sqrt{6 \times 24} = \sqrt{144} = 12$

For the second part we have, mean proportional

$= \sqrt{360 a^{4} \times 250 a^{2} b^{2}} = \sqrt{90000 a^{6} b^{2}} = 300 a^{3} b$

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360 a^{4}

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