Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 7 - Similarity - Chapter Test - Page 483: 11


The geometric mean of $10$ and $15$ is $5 \sqrt 6$.

Work Step by Step

The geometric mean of two numbers is given by the following formula: $\frac{a}{x} = \frac{x}{b}$, where $a$ and $b$ are positive numbers and $x$ is the geometric mean. Let's plug in our numbers: $\frac{10}{x} = \frac{x}{15}$ Use the cross products property to get rid of the fractions: $x^2 = 150$ Rewrite $150$ as the product of a perfect square and another factor: $x^2 = 25 • 6$ Take the positive square root to solve for $x$: $x = 5 \sqrt 6$
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