Contents   Index

Beispiele:

1. $\sqrt{49x^2}=\left\vert 7x\right\vert=7\left\vert x\right\vert=\begin{cases} 7x & \text{falls \(x \geq 0\)} \\ -7x & \text{falls \(x < 0\)} \end{cases}$
2. $\sqrt{a^2-6a+9}=\sqrt{\left(a-3\right)^2}=\left\vert a-3\right\vert=\begin{cases} a-3 & \text{falls $a \geq 3$} -a+3 & \text{falls $a<3$} \end{cases}$
3. Ergänze zu einem vollständigem Quadrat: $\sqrt{t^2-\frac{1}{2}t+...}=\sqrt{t^2-\frac{1}{2}t+\frac{1}{4}}=\sqrt{\left(t-... ...\geq\frac{1}{4}$} \\ -t+\frac{1}{4} & \text{falls $t<\frac{1}{4}$} \end{cases}$
4. $\sqrt{z-7}$, $\mathds{D}=\left\{z\vert z\geq7\right\}$

  Contents   Index