Thursday, December 17, 2009

How do you find the geometric mean between two numbers?

For example, how would you solve:


4 and 9?


16 and 25?


49 and 64?


49 and 100?How do you find the geometric mean between two numbers?
geometric mean, Gm between g1 and g2 is given by





(Gm)^2 = g1*g2





Gm = sqrt(g1*g2)





so Gm between 4 and 9 is





sqrt(4*9) = sqrt(36) = 6





Gm between 16 and 25 is sqrt(16*25) = 20





Gm between 49 and 64 is 56





Gm between 49 and 100 is 70How do you find the geometric mean between two numbers?
you would put


X/4=9/X


then cross multiply leaving you with


X^2=36


take the square root of both leaving you with


X=6





if the answer comes in decimals find the largest whole root number that you can multiply by a number to get the number you trying to square root.


for example let say you got 90 as an answer when u take the square root of that in your last step you will get a decimal answer.


so you find the largest whole root number which is 9 and multiply it by 10 and u get 90 so you would take the square root of 9 which is 3 and leave 10 as square root 10 getting the answer 3(square root 10)
4/x = x/9


CROSS PRODUCTS


x^2 = 36


x= plus or minus 6





16/x=x/25


x^2= 400


x= plus or minus 20





ETC...get it??
The geometric mean between two numbers a and b is the square root of (a times b).
I believe you add the two values and take the square root of the sum.

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