What is the geometric mean of 4 and 12?
(Simplify your answer. Type an exact answer, using radicals as needed.)
(Siser

Question

What is the geometric mean of 4 and 12? $$ \square $$ (Simplify your answer. Type an exact answer, using radicals as needed.) (Siser

UpStudy AI · Accepted Answer

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 $$ \sqrt{48} $$:

$$
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
$$

$$
\boxed{4\sqrt{3}}
$$
The geometric mean of 4 and 12 is $$ 4\sqrt{3} $$.

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