Every real number is either rational or irrational.

$\pi$ is irrational and $\frac{22}{7}$ is rational.

$\left(2\sqrt{3}-5\sqrt{2}\right)+$$\left(\sqrt{3}+2\sqrt{2}\right)=a(\sqrt{b}-\sqrt{c})$. Find the value of $a$

$\left(2\sqrt{2} + 5\sqrt{3}-7\sqrt{5}\right)+$ $\left(3\sqrt{3}-\sqrt{2}+\sqrt{5}\right)=\sqrt{x}+a\sqrt{y}-b\sqrt{z}$. Find the value of $a-b$

If $\left(\frac{2}{3}\sqrt{7}-\frac{1}{2}\sqrt{2}+6\sqrt{11}\right)$  $+\left(\frac{1}{3}\sqrt{7}+\frac{3}{2}\sqrt{2}-\sqrt{11}\right)=\sqrt{a}+\sqrt{b}+c\sqrt{d}$. Find the value of $c$.

If $16\sqrt{6}$ $÷4\sqrt{2}=k\sqrt{2}$. Find the value of $k$

Simplify:

$\left(4+\sqrt{2}\right)\left(4-\sqrt{2}\right)$

Simplify:

$\left(-3+\sqrt{5}\right)\left(-3-\sqrt{5}\right)$

 If ${\left(3-\sqrt{3}\right)}^2=A-B\sqrt{a}$ . Find the value of $A$.