Chapter 8.1, Problem 15CE

a.

To determine

To find: the geometric mean of the given two numbers

Answer to Problem 15CE

The geometric mean between the two given numbers is $\sqrt{6}$

Explanation of Solution

Given Information: Two numbers 2 and 3.

Formula Used:

The geometric mean between two numbers a and b is defined by the relation,

  $c=\sqrt{ab}$

Calculation:

For the numbers 2 and 3,the geometric mean can be calculated using the given formula as,

  $\begin{array}{c}c=\sqrt{2\times 3}\\ =\sqrt{6}\end{array}$

b.

To determine

To find: the geometric mean of the given two numbers

Answer to Problem 15CE

The geometric mean between the two given numbers is $2\sqrt{3}$

Explanation of Solution

Given Information: Two numbers 2 and 6.

Formula Used:

The geometric mean between two numbers a and b is defined by the relation,

  $c=\sqrt{ab}$

Calculation:

For the numbers 2 and 6,the geometric mean can be calculated using the given formula as,

  $\begin{array}{c}c=\sqrt{2\times 6}\\ =\sqrt{12}\\ =2\sqrt{3}\end{array}$

c.

To determine

To find: the geometric mean of the given two numbers

Answer to Problem 15CE

The geometric mean between the two given numbers is $10$

Explanation of Solution

Given Information: Two numbers 4 and 25.

Formula Used:

The geometric mean between two numbers a and b is defined by the relation,

  $c=\sqrt{ab}$

Calculation:

For the numbers 4 and 25,the geometric mean can be calculated using the given formula as,

  $\begin{array}{c}c=\sqrt{4\times 25}\\ =\sqrt{100}\\ =10\end{array}$