Disequazione irrazionale $\sqrt{x+3}<2$

Text

Solve the irrational inequality $\sqrt{x+3}<2.$

Solution

Existence condition: $x+3\ge 0\implies x\ge -3$. The right-hand side is positive and the root is non-negative, so we may square: $x+3<4\implies x<1.$ Intersecting with the existence condition: $\boxed{-3\le x<1.}$