<s>[INST] $\sqrt{m^2 - x^2} \leq x , m > 0$ the range for $x$ is? $\sqrt{m^2 - x^2} \leq x $
$\sqrt{{m}^{2} - {x}^{2}} \geq 0$
$x \geq 0$
$\sqrt{m^2 - x^2} \leq x $
$m^2 - x^2 \leq x^2 $
$m^2 \leq 2x^2$
$\frac{m}{\sqrt 2} \leq x$
$\sqrt{{m}^{2} - {x}^{2}} \geq 0$
${m}^{2} \geq {x}^{2}$
$m > 0, x > 0$
$m \geq x$
$x \leq m$
$\frac{m}{\sqrt 2} \leq x \leq m$
is it right?
 [/INST] Let $0<x<m^2$, tthe squaring we get
$$m^2-x^2 \ge x^2 \implies  0\le x \le m/\sqrt{2}$$
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