Respuesta :
Answer:
The Geometric Mean of 4 and 12 is 6.9
Step-by-step explanation:
Given Numbers are 4 and 12
To find : Geometric mean of the given No.
The Geometric Mean is a type of average where we multiply the nos. together and then take a square root (for two nos), cube root (for three nos) etc.
Formula for Geometric Mean is given by,
[tex]Geometric\,Mean\,of\,x_1\,,\,x_2\,,\,x_3..x_n=\sqrt[n]{x_1\times x_2\times x_3\times\,...\,\times x_n}[/tex]
⇒ Geometric Mean of 4 and 12 = [tex]\sqrt{4\times12}[/tex]
= [tex]\sqrt{48}[/tex]
= [tex]4\sqrt{3}[/tex]
= 6.92820323028
= 6.9
Therefore, The Geometric Mean of 4 and 12 is 6.9
The geometric mean of 4 and 12 is 6.93
The geometric mean of a given set of numbers can be calculated using the formula
[tex]\bar{x}_{geom}=\sqrt[n]{x_{1} \times x_{2} \times x_{3} \times ... \times x_{n} }[/tex]
Where [tex]n[/tex] is the number of terms
From the question,
We are to determine the geometric mean of 4 and 12
That is,
n =2
∴ The geometric mean of the numbers = [tex]\sqrt{4 \times 12}[/tex]
The geometric mean of the numbers = [tex]\sqrt{48}[/tex]
The geometric mean of the numbers = 6.93
Hence, the geometric mean of 4 and 12 is 6.93
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