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Question

# Find the geometric mean of the two numbers. 14 and 20.

Solution

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Step 1
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Determine the geometric mean.

\begin{align*} x^{2} &= ab && \text{Definition of geometric mean}\\ x^{2} &= 14 \cdot 20 && \text{Substitute}\\ x &= \sqrt{14 \cdot 20} && \text{Take positive square root of each side}\\ x &= \sqrt{280} && \text{Multiply}\\ x &= \sqrt{4 \cdot 70} && \text{Factor}\\ x &= 2\sqrt{70} && \text{Simplify} \end{align*}

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