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} \\\\\\ √(270)=x\implies √(30\cdot 3^2)=x\implies 3√(30)=x`

Answer 2

Geometric Mean = 16.431 or the radical form in the picture