Question

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Answer 1

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Answer 2

Question :-

Find the mean proportional between $\frac{1}{2} \:\:and\:\: \frac{1}{72}$.

Formula :-

Mean proportional = $\sqrt{ab}$,

where a and b are two integers.

Solution :-

Here, a $=\frac{1}{2} \:\:and\:\:b=\frac{1}{72}$

$Mean\:\:proportional =\sqrt{ab}\\\\= \sqrt{\frac{1}{2} \times\frac{1}{72} } \\\\=\sqrt{\frac{1}{144} } \\\\=\frac{1}{12}$

144 is the square of 12 and 1 is the square of 1.

So, $\sqrt{1} =1\:\: and\:\:\sqrt{144} =12$

Therefore, the mean proportional between $\frac{1}{2} \:\:and\:\: \frac{1}{72}$ is $\frac{1}{12}$.

Answer :-

The mean proportional between $\frac{1}{2} \:\:and\:\: \frac{1}{72}$ is $\frac{1}{12}$.

More Information:-

$\star$ Mean proportional of two numbers is the square root of the product of that two numbers.

$\star$ Derivation the formula of Mean proportional of two numbers :-

Let Mean proportional of two numbers a and b be m.

Then, a : m :: m : b

$=>\frac{a}{m}=\frac{m}{b}$

$=>m^{2} = ab \:\:\:\:\:\:\:\:\:\:[By\:\:Cross-Multiplication]\\\\=>m=\sqrt{ab}$