Question

What is geometric mean proportion between 30+200 and 54-648

Answer 1

What is geometric mean proportion between 30+200 and 54-648

Answer 2

The geometric mean proportion between $30+\sqrt{200}$ and $54-\sqrt{648}$  is $6\sqrt{35}$

Step-by-step explanation:

To find : The geometric mean proportion between $30+\sqrt{200}$ and $54-\sqrt{648}$ ?

Solution :

The geometric mean proportion between two number a and b is given by, $GM(a,b) = \sqrt{a\times b}$

Here, $a=30+\sqrt{200}$ and $b=54-\sqrt{648}$

Substitute the values,

$GM(30+\sqrt{200},54-\sqrt{648})=\sqrt{(30+\sqrt{200})\times(54-\sqrt{648})}$

$GM(30+\sqrt{200},54-\sqrt{648})=\sqrt{30\times54-30\times \sqrt{648}+\sqrt{200}\times54-\sqrt{200}\times \sqrt{648}}$

$GM(30+\sqrt{200},54-\sqrt{648})=\sqrt{1620-30\times 18\sqrt{2}+10\sqrt{2}\times54-18\sqrt{2}\times 10\sqrt{2}}$

$GM(30+\sqrt{200},54-\sqrt{648})=\sqrt{1620-540\sqrt{2}+540\sqrt{2}-360}$

$GM(30+\sqrt{200},54-\sqrt{648})=\sqrt{1260}$

$GM(30+\sqrt{200},54-\sqrt{648})=6\sqrt{35}$

Therefore, The geometric mean proportion between $30+\sqrt{200}$ and $54-\sqrt{648}$  is $6\sqrt{35}$

#Learn more

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