The RMS-AM inequality states that for positive real numbers $x_1,\ldots,x_n$, $$AM=\frac{x_1+\cdots+x_n}{n}\leq\sqrt{\frac{x_1^2+\cdots+x_n^2}{n}}=RMS.$$ For two positive numbers $x_1,x_2$, the inequality can be inferred geometrically from the diagram below.
Unless I'm mistaken, the picture also seems to imply that for two positive numbers $x_1,x_2$,
$$RMS^2\leq 2\cdot AM^2$$
so that $$AM=\frac{x_1+x_2}{2}\geq\frac{1}{\sqrt2}\sqrt{\frac{x_1^2+x_2^2}{2}}=\frac{1}{\sqrt2}RMS.$$
Is anyone aware of how this might generalise for more than two numbers?