Question

Give the geometric mean between:

a. $2$ and $3$ b. $2$ and $6$ c. $4$and $25.$

Short answer

1. The final answer is $\sqrt{6}.$

Step-by-step solution

Step 1. Given information:

The given numbers are $2,3$ .

Step 2. Concept use.

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

$c=\sqrt{ab}$

Step 3. Applying the concept.    

By using the formula for the given numbers.

$c=\sqrt{2\times 3}$

$=\sqrt{6}$

Therefore, the geometric mean of the numbers is $\sqrt{6}$.

b. The final answer is $2\sqrt{3.}$

Step 1. Given information:

The given numbers are $2,6$ .

Step 2. Concept use.

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

$c=\sqrt{ab}$

Step 3. Applying the concept.    

By using the formula for the given numbers.

$c=\sqrt{2\times 6}$

$=\sqrt{12}$

$=2\sqrt{3}$

Therefore, the geometric mean of the numbers is $2\sqrt{3}$.

c. The final answer is $10.$

Step 1. Given information:

The given numbers are $4,25.$

Step 2. Concept use.

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

$c=\sqrt{ab}$

Step 3. Applying the concept.    

By using the formula for the given numbers.

$c=\sqrt{4\times 25}$

$=\sqrt{100}$

$=10$

Therefore, the geometric mean of the numbers is $10.$.