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 \( 4.2 \).
1 answer