Question
What is the geometric mean of 4 and 12? \( \square \) (Simplify your answer. Type an exact answer, using radicals as needed.) (Siser
Ask by Dawson Schofield. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The geometric mean of 4 and 12 is \( 4\sqrt{3} \).
Solution
The geometric mean of two numbers \( a \) and \( b \) is given by the square root of their product:
\[
\text{Geometric Mean} = \sqrt{a \times b}
\]
For \( a = 4 \) and \( b = 12 \):
\[
\text{Geometric Mean} = \sqrt{4 \times 12} = \sqrt{48}
\]
Simplify \( \sqrt{48} \):
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]
\[
\boxed{4\sqrt{3}}
\]
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Simplify this solution Mind Expander
To find the geometric mean of two numbers, you use the formula: \[ \text{Geometric Mean} = \sqrt{a \times b} \] In this case, \( a = 4 \) and \( b = 12 \). Now plug in the values: \[ \text{Geometric Mean} = \sqrt{4 \times 12} = \sqrt{48} \] Next, simplify \( \sqrt{48} \): \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \] So, the geometric mean of 4 and 12 is \( 4\sqrt{3} \).
