Chapter 8: Q15. (page 288)

Give the geometric mean between:
a. $2$ and $3$ b. $2$ and $6$ c. $4$ and $25 .$

Short Answer

Expert verified

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,

$c = \sqrt{a b}$

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,

$c = \sqrt{a b}$

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,

$c = \sqrt{a b}$

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 $10 .$ .

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Give the geometric mean between:
a. $2$ and $3$ b. $2$ and $6$ c. $4$ and $25 .$

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Concept use.

Step 3. Applying the concept.

Step 1. Given information:

Step 2. Concept use.

Step 3. Applying the concept.

Step 1. Given information:

Step 2. Concept use.

Step 3. Applying the concept.

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Give the geometric mean between:a. 2 and 3 b. 2 and 6 c. 4and 25.

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Concept use.

Step 3. Applying the concept.

Step 1. Given information:

Step 2. Concept use.

Step 3. Applying the concept.

Step 1. Given information:

Step 2. Concept use.

Step 3. Applying the concept.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Give the geometric mean between:
a. $2$ and $3$ b. $2$ and $6$ c. $4$ and $25 .$