$2 \sqrt{3} + \sqrt{3}$ is equal to

Construct the square root spiral up to $\sqrt{6}$.

Insert a rational number and an irrational number between the following:
$\frac{-2}{5}$ and $\frac{1}{2}$

Rationalise the denominator of the following expression and evaluate it by taking $\sqrt{2}=1.414, \sqrt{3}=1.732$,and $\sqrt{5}=2.236$ up to three decimal places:
$\frac{\sqrt{2}}{2+\sqrt{2}}$

Calculate the sum: $0. \overline{3} + 0.4 \overline{7}$

If $x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$ and $y=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}},$ then find the value of $x^{2}+y^{2}$.