To find the geometric mean of two numbers, we use the formula for the geometric mean:
[tex]\[
\text{Geometric mean} = \sqrt{a \times b}
\][/tex]
In this problem, the numbers given are \( a = 6 \) and \( b = 7 \).
Let's calculate the geometric mean step-by-step:
1. Multiply the two numbers:
[tex]\[
a \times b = 6 \times 7 = 42
\][/tex]
2. Take the square root of the product:
[tex]\[
\sqrt{42}
\][/tex]
The geometric mean of 6 and 7 is \(\sqrt{42}\).
Among the given choices:
A. \(\sqrt{42}\)
B. \(4 \sqrt{3}\)
C. 7
D. 42
The correct answer is:
[tex]\[
\boxed{\sqrt{42}}
\][/tex]
