find the geometric mean of 4 and 10

ANSWER

[tex]Geometric \: \: Mean=2 \sqrt{10} [/tex]

EXPLANATION

The geometric mean for two real numbers,
x and y, where
[tex]xy \geqslant 0[/tex]
is by

[tex]Geometric \: \: Mean= \sqrt{xy} [/tex]

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

[tex]Geometric \: \: Mean= \sqrt{4 \times 10} [/tex]

[tex]Geometric \: \: Mean= \sqrt{4} \times \sqrt{10} [/tex]

[tex]Geometric \: \: Mean=2 \sqrt{10} [/tex]

Or

[tex]Geometric \: \: Mean=6.3[/tex] to the nearest tenth.