Question

find the geometric mean of 4 and 10

Answer 1

ANSWER

$Geometric \: \: Mean=2 \sqrt{10}$

EXPLANATION

The geometric mean for two real numbers,
x and y, where
$xy \geqslant 0$
is by

$Geometric \: \: Mean= \sqrt{xy}$

We apply this formula to find the geometric mean of 4 and 10 to be,

$Geometric \: \: Mean= \sqrt{4 \times 10}$

$Geometric \: \: Mean= \sqrt{4} \times \sqrt{10}$

$Geometric \: \: Mean=2 \sqrt{10}$

Or

$Geometric \: \: Mean=6.3$ to the nearest tenth.

Answer 2

The geometric mean of 4 and 10 is 6.3.

Geometric mean is a mean which indicates the central tendency of a group of numbers by using the product of their values.

The geometric mean is given by:

$Geometric\ mean=\sqrt[n]{\pi (x_i)}\\\\i=1,2,3,.\ .\ .$

The geometric mean of 4 and 10 is:

$Geometric \ mean=\sqrt{4*10}=6.3$

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