Sum of two surd is always a surd.

True or false :

$\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}+\sqrt{\mathrm{c}}=\sqrt{\mathrm{a}+\mathrm{b}+\mathrm{c}}$

$\sqrt{\mathrm{a}}·\sqrt{\mathrm{b}}=\sqrt{\mathrm{a}·\mathrm{b}}$.

$\sqrt{\mathrm{a}}(\sqrt{x}+\sqrt{y})=\sqrt{\mathrm{a}x}+\sqrt{\mathrm{a}y}$.

The two surds $2\sqrt{3}$ and $\frac{1}{2\sqrt{3}}$ are conjugate to each other.

The reciprocal of the surd $\left(2+\sqrt{3}\right)$ is $\left(2-\sqrt{3}\right)$.

$\sqrt{\mathrm{a}\left(\mathrm{b}+\mathrm{c}\right)}=\sqrt{\mathrm{ab}}+\sqrt{\mathrm{ac}}$.

True or false :

$\frac{x^2-3}{\sqrt{x}+\sqrt{3}}=\sqrt{x}-\sqrt{3}$

True or false :

$\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\sqrt{2}$