The mean proportional of $6$ and $24$ is ______________

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Solution

$\begin{matrix} L e t a = 6 b = 24 m e a n p r o p o r t i o n a l = \sqrt{a \times b} = \sqrt{6 \times 24} = 12 o r \frac{a}{c} = \frac{c}{b} c^{2} = \sqrt{a b} c = m e a n p r o p o r t i o n a l = \sqrt{6 \times 24} = 12 \end{matrix}$

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6

24

6

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Find the mean proportional between:
$(i)$ $6$ and $24$
$(i i)$ $3$ and $27$
$(i i i)$ $0.4$ and $0.9$

(1) 6

24

(2) 360 a^{4}

250 a^{2} b^{2}

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