Question

Find the geometric mean of 15 and 18. Write the exact answer.

Answer 1

$\bf \stackrel{geometric~mean}{\cfrac{15}{x}=\cfrac{x}{18}}\implies 15\cdot 18=x^2\implies 270=x^2~~ \begin{cases} 270=2\cdot 3\cdot 3\cdot 3\cdot 5\\ \qquad 2\cdot 3^2\cdot 3\cdot 5\\ \qquad 30\cdot 3^2 \end{cases} \\\\\\ \sqrt{270}=x\implies \sqrt{30\cdot 3^2}=x\implies 3\sqrt{30}=x$

Answer 2

Geometric Mean = 16.431 or the radical form in the picture