If $\sqrt{2}=1.4142,$ then $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$ is equal to

Fill in the blanks so as to make each of the following statements true (Final answer only)

$\sqrt{7}$ is a / an $\ldots \ldots \ldots$ number.

If $a=5+2 \sqrt{6}$ and $b=\frac{1}{a},$ then what will be the value of $a^{2}+b^{2} ?$

Find the values of $a$ and $b$ in each of the following:

$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+\frac{7}{11} \sqrt{5} b$

If $a=\frac{3+\sqrt{5}}{2},$ then find the value of $a^{2}+\frac{1}{a^{2}}$.

Simplify the following:

$4 \sqrt{28} \div 3 \sqrt{7}$