Question

Use the geometric mean to find x. Round your answer to the nearest tenth. (1 point)
x is the line between 6 and 3

Answer 1

To find \( x \) using the geometric mean of the numbers 6 and 3, you can use the formula for the geometric mean:

\[
x = \sqrt{a \cdot b}
\]

where \( a \) and \( b \) are the two numbers.

In this case, \( a = 6 \) and \( b = 3 \). So we calculate:

\[
x = \sqrt{6 \cdot 3} = \sqrt{18}
\]

Now, we simplify \( \sqrt{18} \):

\[
\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}
\]

Now we can approximate \( \sqrt{2} \) (which is approximately 1.414):

\[
x \approx 3 \cdot 1.414 \approx 4.242
\]

Rounding to the nearest tenth, we have:

\[
x \approx 4.2
\]

So, the value of \( x \) is approximately \( 4.2 \).