Use the geometric mean to solve for the value of x. Round your answer to the nearest tenth. (1 point)

3
4

1 answer

To find the value of \( x \) using the geometric mean of the numbers 3 and 4, we can use the formula for the geometric mean, which is given by:

\[ \text{Geometric Mean} = \sqrt{a \times b} \]

where \( a = 3 \) and \( b = 4 \).

Now, let's calculate the geometric mean:

\[ \text{Geometric Mean} = \sqrt{3 \times 4} = \sqrt{12} \]

Next, we can simplify \( \sqrt{12} \):

\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]

Now we can calculate the numerical value of \( 2\sqrt{3} \). Since \( \sqrt{3} \approx 1.732 \):

\[ 2\sqrt{3} \approx 2 \times 1.732 \approx 3.464 \]

Rounding to the nearest tenth:

\[ 3.464 \approx 3.5 \]

Therefore, the value of \( x \) is approximately:

\[ \boxed{3.5} \]