right triangles,the geometric mean help please

[hailstone]

hello
teen father needs help on geometric mean. this doggone Merrill Geometry book dose not seem to give a example of how to figure out the process for geomertic mean for a fraction. my daughter knows thank god, the formula for whole numbers. Could someone show me the formula to these questions under Right triangles and trig.
thanks in advance.

3/8 and 8/3 we know its 1 from the anwers but the formula to get to 1

also
1/2 and 2/3

1/4 and 9 we know from the anwsers its 3/2

4 and 1/9

 

[Gene]

The geometric mean of n numbers is the n^th root of the product. Don't let fractions throw you.
(3/8)*(8/3) = 1
Two numbers so it is square root of 1 = 1.

sqrt((1/2)(2/3))=sqrt(1/3) = 1/sqrt(3) = sqrt(3)/3 (your choice.)

sqrt((1/4)(9)) = sqrt(9/4) = 3/2

sqrt(4*(1/9))=sqrt(4/9) = 2/3

 

[hailstone]

gene, thank you for helping us on that question we couldn't figure it out even though it was that simple.
what i we couldn't get was how to do geometric mean witha fractions.
i will be coming back to this wed site when i need more help so thanks again.
love the teen daughter