To find the value of \( x \) using the geometric mean of the numbers 5 and 12, we use the formula for the geometric mean:
\[ x = \sqrt{a \cdot b} \]
where \( a = 5 \) and \( b = 12 \).
Calculating this:
\[ x = \sqrt{5 \cdot 12} = \sqrt{60} \]
Now calculate \( \sqrt{60} \):
\[ \sqrt{60} \approx 7.75 \]
So the correct response for the value of \( x \) using the geometric mean is:
7.75