$$\forall x,y\in \mathbb{R}: \ \sqrt{x^2+y^2}=x+y$$

$$\forall x,y\in \mathbb{R}: \ x^2-2xy+y^2 \ge 0 $$

$$\forall x\in \mathbb{R}, x\ge 0: \ \sqrt{x^2+x}=\sqrt{x}\sqrt{x+1}$$

$$\forall x,y\in \mathbb{R}_{>0}: \ \frac{\sqrt[3]{x}}{2\sqrt[3]{y}}=\left(\frac x{8y}\right)^{\frac 13}$$

$$\forall x,y\in \mathbb{R}\setminus\{0\}: \ \frac{\quad x \quad}{\frac 3y} = \frac{3}{xy} $$

$$\forall x,y\in \mathbb{R}: \ \sqrt{x^2(y^2+1)}=x\sqrt{y^2+1}$$