+0

# what is the geometric mean of 10 and 30

0
305
4

what is the geometric mean of 10 and 30

Guest Feb 14, 2015

#3
+26399
+10

The geometric mean only applies to positive numbers.

It has a geometric interpretation.  Image a rectangle with sides 10 and 30.  It has an area of 300.  A square of side √(10*30), i.e. one with side lengths equal to the geometric mean of the two rectangle lengths, has the same area.

Similarly, for higher order geometric means. e.g. a cuboid with side lengths u, v and w has the same volume as a cube with side lengths 3√(u*v*w), etc.

.

Alan  Feb 14, 2015
Sort:

#1
+80875
+10

The geometric mean of N numbers is just the Nth root of their product.....so, since we have two numbers, we have....

√(10 * 30) = √300 = 10√3

CPhill  Feb 14, 2015
#2
+91436
+5

SO

The geometric mean of 7,6,8 and 2

is it   $$\sqrt[4]{7*6*8*2}$$

$${\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{2}}\right)}^{\left({\mathtt{0.25}}\right)} = {\mathtt{5.091\: \!459\: \!790\: \!043\: \!661}}$$

what happen if there is negative numbers?

Melody  Feb 14, 2015
#3
+26399
+10

The geometric mean only applies to positive numbers.

It has a geometric interpretation.  Image a rectangle with sides 10 and 30.  It has an area of 300.  A square of side √(10*30), i.e. one with side lengths equal to the geometric mean of the two rectangle lengths, has the same area.

Similarly, for higher order geometric means. e.g. a cuboid with side lengths u, v and w has the same volume as a cube with side lengths 3√(u*v*w), etc.

.

Alan  Feb 14, 2015
#4
+91436
0

Thanks Alan

Melody  Feb 15, 2015

### 20 Online Users

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The text passage contains a single mathematical question and an answer provided by a user. The question asks for the geometric mean of 10 and 30, and the answer is given as \( \sqrt{300} = 10\sqrt{3} \).
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
+0

# what is the geometric mean of 10 and 30

0
305
4

what is the geometric mean of 10 and 30

Guest Feb 14, 2015

#3
+26399
+10

The geometric mean only applies to positive numbers.

It has a geometric interpretation.  Image a rectangle with sides 10 and 30.  It has an area of 300.  A square of side √(10*30), i.e. one with side lengths equal to the geometric mean of the two rectangle lengths, has the same area.

Similarly, for higher order geometric means. e.g. a cuboid with side lengths u, v and w has the same volume as a cube with side lengths 3√(u*v*w), etc.

.

Alan  Feb 14, 2015
Sort:

#1
+80875
+10

The geometric mean of N numbers is just the Nth root of their product.....so, since we have two numbers, we have....

√(10 * 30) = √300 = 10√3

CPhill  Feb 14, 2015
#2
+91436
+5

SO

The geometric mean of 7,6,8 and 2

is it   $$\sqrt[4]{7*6*8*2}$$

$${\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{2}}\right)}^{\left({\mathtt{0.25}}\right)} = {\mathtt{5.091\: \!459\: \!790\: \!043\: \!661}}$$

what happen if there is negative numbers?

Melody  Feb 14, 2015
#3
+26399
+10

The geometric mean only applies to positive numbers.

It has a geometric interpretation.  Image a rectangle with sides 10 and 30.  It has an area of 300.  A square of side √(10*30), i.e. one with side lengths equal to the geometric mean of the two rectangle lengths, has the same area.

Similarly, for higher order geometric means. e.g. a cuboid with side lengths u, v and w has the same volume as a cube with side lengths 3√(u*v*w), etc.

.

Alan  Feb 14, 2015
#4
+91436
0

Thanks Alan

Melody  Feb 15, 2015

### 20 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details
user
The text passage contains a single mathematical question and an answer provided by a user. The question asks for the geometric mean of 10 and 30, and the answer is given as \( \sqrt{300} = 10\sqrt{3} \).

TYPE: SINGLE_QUESTION_WITH_ANSWER