Chapter 8: Q19. (page 288)

Find the geometric mean between the two numbers.
$1$ and $1000$

Short Answer

Expert verified

Geometric mean is $10 \sqrt{10}$ .

Step by step solution

Step 1. Given information.

The given two numbers are,

$1$ and $1000$

Geometric mean between two numbers $a$ and $b$

$r = \sqrt{a_{1} \times a_{2}}$

Here,

$\begin{matrix} a_{1} = 1 \\ a_{2} = 1000 \end{matrix}$

Step 3. Calculate the mean.

Mean $= \sqrt{a_{1} \times a_{2}}$

$\begin{matrix} \sqrt{1 \cdot 1000} = \sqrt{1000} \\ = \sqrt{100 \cdot 10} \\ = \sqrt{100} \cdot \sqrt{10} \\ = 10 \sqrt{10} \end{matrix}$

Step 4. Neglect negative sign.

Since, square root is positive quantity.

Therefore, the geometric mean between the two numbers $1$ and $1000$ is $10 \sqrt{10}$ .

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Find the geometric mean between the two numbers.
$1$ and $1000$

Short Answer

Step by step solution

Step 1. Given information.

Step 3. Calculate the mean.

Step 4. Neglect negative sign.

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Find the geometric mean between the two numbers.1 and 1000

Short Answer

Step by step solution

Step 1. Given information.

Step 3. Calculate the mean.

Step 4. Neglect negative sign.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Decision Maths

Mechanics Maths

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find the geometric mean between the two numbers.
$1$ and $1000$