Finding Mean Proportional Between 0.06 and 6

The question asks us to find the mean proportional between the numbers 0.06 and 6. The mean proportional, also known as the geometric mean, between two numbers '$a$' and '$b$' is a number '$x$' such that the ratio of '$a$' to '$x$' is the same as the ratio of '$x$' to '$b$'.

Understanding Mean Proportional

Mathematically, if '$x$' is the mean proportional between '$a$' and '$b$', it satisfies the proportion:

$$ \frac{a}{x} = \frac{x}{b} $$

Cross-multiplying gives us:

$$ x^2 = a \times b $$

Therefore, the mean proportional '$x$' can be found by taking the square root of the product of the two numbers:

$$ x = \sqrt{a \times b} $$

Calculation Steps

In this problem, we have:

• $a = 0.06$
• $b = 6$

Now, we substitute these values into the formula:

$$ x = \sqrt{0.06 \times 6} $$

First, calculate the product of 0.06 and 6:

$$ 0.06 \times 6 = 0.36 $$

Next, find the square root of the product:

$$ x = \sqrt{0.36} $$

The square root of 0.36 is 0.6:

$$ x = 0.6 $$

Result Analysis

The calculated mean proportional between 0.06 and 6 is 0.6.

Comparing this result with the given options:

• Option 1: 0.06
• Option 2: 0.6
• Option 3: 60
• Option 4: 6

The calculated value, 0.6, matches Option 2.