= Solution
\b[The squared <angular momentum> and one chosen component can have simultaneously sharp values. All three components cannot have simultaneously sharp values in a nonzero-$j$ state.] The possible measured component values are $m\hbar$, while the squared magnitude is $j(j+1)\hbar^2$. This concerns the <quantum state>, rather than imperfect experimental resolution. The <Robertson uncertainty relation>, for example,
$$
\Delta j_x\,\Delta j_y\geq\frac{\hbar}{2}|\langle\hat j_z\rangle|,
$$
quantifies the restriction; its right-hand side may vanish in some states, without making all three components simultaneously sharp.
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