Question

Find the geometric mean of the numbers. If necessary, give the awnser in simplest form. 2/3 and 1/2.

The geometric mean is ____

Answer 1

0.577

Explanation:

We are given the following two numbers and we are to find their geometric mean:

`\frac {2} {3}` and
`\frac {1} {2}`

We know the formula for finding the geometric mean:

Geometric mean =
`\sqrt[n]{a_1.a_2.a_3...a_n}`

So putting in the given values in the above formula to get:

Geometric mean =
`\sqrt [2] {\frac {2} {3} .\frac {1} {2}  }` =
`\sqrt {\frac {1} {3} }`

Geometric mean = 0.577

Answer 2

Geometric mean = 1/√3 or 0.58

Explanation:

We have to find the geometric mean of the 2/3 and 1/2.

To find the geometric mean of n terms we use the formula

Geometric mean =
`\sqrt[n]{a_(1)* a_(2)* a_(3)....a_(n)}`

By putting the values in the formula

Geometric mean
`=\sqrt{(2)/(3)* (1)/(2)}`

`\sqrt{(2)/(6)}=(1)/(√(3) )`

geometric mean = 0.58