Question

find the geometric mean of 10,40 & 160

Answer 1

Geometric mean of a and b=(ab)^1/2

Geometric mean of abc=[(abc)^1/2]^3

Geometric mean=(abc)^3/2

=(10×40×60)^3/2=(10×40×60)^1/2

(10 40 60)

Cube root/3rd root)

=(2×5×2×2×2×5×2×2×5×3)

=(2^6×5^3×3)^3/2)

=2^2×5×3^1/3

20×3^1/3.

Answer 2

The geometric mean of 10 , 40 & 160 is 40

Given :

The numbers 10 , 40 & 160

To find :

The geometric mean of 10 , 40 & 160

Solution :

Step 1 of 2 :

Write down the given numbers

Here the given numbers are 10 , 40 & 160

Step 2 of 2 :

Find geometric mean of 10 , 40 & 160

We know that for a given set of n numbers geometric mean is defined as nth root of the product of n numbers

The required geometric mean

$\displaystyle \sf{ = \sqrt[3]{10 \times 40 \times 160} }$

$\displaystyle \sf{ = \sqrt[3]{(2 \times 5) \times (2 \times 2 \times 2 \times 5) \times (2 \times 2 \times 2 \times 2 \times 2 \times 5)} }$

$\displaystyle \sf{ = \sqrt[3]{ {2}^{3} \times {2}^{3} \times {2}^{3} \times {5}^{3} } }$

$\displaystyle \sf{ = 2 \times 2 \times 2 \times 5}$

$\sf = 40$

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