Question

find the mean proportional between 3and 27​

Answer 1

Step-by-step explanation:

$b ^{2} = ac \\ b = \sqrt{ac} \\ b = \sqrt{3 \times 27} \\ \sqrt{81} \\ 9$

Answer 2

Step-by-step explanation:

Given :-

3 and 27

To find :-

Find the Mean Proportional between them ?

Solution :-

General Method :-

Given numbers are 3 and 27

Let the Mean Proportional between them be X

therefore, 3:X :: X:27

The product of Means = X×X = X²

The product of extremes = 3×27 = 81

We know that

In proportion, Product of means= Product of extremes

=> X² = 81

=> X=±√81

=> X = ±9

Since the given numbers are positive then

X = 9

So ,Mean Proportional = 9

Shortcut Method:-

The Mean Proportional between a and b is √(ab)

So we have

a = 3

b = 27

Mean Proportional = √(3×27)

=> √81

=> 9

Answer:-

The Mean Proportional between 3 and 27 is 9

Used formulae:-

• In proportion, Product of means= Product of extremes

• The Mean Proportional between a and b is √(ab)