Question

The geometric mean proportion between $30 + \sqrt{200}$ and $54 - \sqrt{648}$ is:

Accepted Answer

C. Simplify terms: $30 + \sqrt{200} = 30 + 10\sqrt{2} = 10(3 + \sqrt{2})$. $54 - \sqrt{648} = 54 - 18\sqrt{2} = 18(3 - \sqrt{2})$. Geometric mean $GM = \sqrt{10(3 + \sqrt{2}) 	imes 18(3 - \sqrt{2})} = \sqrt{180 	imes (3^2 - (\sqrt{2})^2)} = \sqrt{180 	imes 7} = \sqrt{1260} = 6\sqrt{35}$.

Geometric mean of radical expressions

Explanation

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