finding the geometric mean

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darkside55

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Dec 2, 2019
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help for geometry part one.PNGshowing my work.PNGim stuck because im not sure how im supposed to solve this and my work is highlighted/ outlined in yellow i want to make sure i have the right answers for these.
 
Please explain the reason for the "or". You appear to be moving the 2 from the index of the radical (where it is optional) to a multiplier (which changes the answer). Why?

Do you understand that [MATH]\sqrt[2]{x}[/MATH] means the same thing as [MATH]\sqrt{x}[/MATH], but is not the same as [MATH]2\sqrt{x}[/MATH]?

The geometric mean of [MATH]a[/MATH] and [MATH]b[/MATH] is defined as [MATH]\sqrt{ab}[/MATH].
 
Dr. Peterson just defined it.
Geometric mean is the middle value in a geometric sequence.

For example:
In 2,4,8 the geometric mean is 4.
In 1/4, 1/16, and 1/64, the geometric mean is 1/16.
 
firemath said:
Dr. Peterson just defined it.
Geometric mean is the middle value in a geometric sequence.

For example:
In 2,4,8 the geometric mean is 4.
In 1/4, 1/16, and 1/64, the geometric mean is 1/16.
Click to expand...
I should've been clearer - I was asking OP to define it.
 
Dr.Peterson said:
Please explain the reason for the "or". You appear to be moving the 2 from the index of the radical (where it is optional) to a multiplier (which changes the answer). Why?

Do you understand that [MATH]\sqrt[2]{x}[/MATH] means the same thing as [MATH]\sqrt{x}[/MATH], but is not the same as [MATH]2\sqrt{x}[/MATH]?

The geometric mean of [MATH]a[/MATH] and [MATH]b[/MATH] is defined as [MATH]\sqrt{ab}[/MATH].
Click to expand...
i was placing the or because im not sure which equation is correct, and yes i am aware
 
To simplify square roots, break things down into prime factors and see if you can rearrange into squares

[MATH]\sqrt{3 * 48} = \sqrt{2 * 2 * 2 * 2 * 3 * 3} = \sqrt{2^4 * 3^2} = \sqrt{(2^2)^2 * 3^2} = 2^2 * 3 = 4 * 3 = 12.[/MATH]
 
Again, why are you not sure? Do you know the definition of "geometric mean". Do you understand the difference between \(\displaystyle \sqrt[2]{x}\) and \(\displaystyle 2\sqrt{x}\)?
 
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