The expression \(\sqrt{-10b}\) involves a square root, which is defined for non-negative numbers in the real number system. This means that the expression inside the square root (the radicand) must be greater than or equal to zero. Therefore, we need to set up the inequality:
\[ -10b \geq 0 \]
To solve for \(b\), we can divide both sides by \(-10\). Remember that when we divide or multiply both sides of an inequality by a negative number, we need to reverse the inequality sign:
\[ b \leq 0 \]
Thus, for the expression \(\sqrt{-10b}\) to be defined in the real numbers, the value of \(b\) must be less than or equal to \(0\).
In summary, the values of \(b\) for which the expression makes sense are:
\[ b \leq 0 \]