The number obtained on rationalizing the denominator of $\frac{1}{7-\sqrt{2}}$ is

Find the value of the following expression correct to three decimal places,rationalizing the denominator if needed. Take $\sqrt{2} = 1.414$,$\sqrt{3} = 1.732$,and $\sqrt{5} = 2.236$.
$\frac{4}{3 \sqrt{3}-2 \sqrt{2}} + \frac{3}{3 \sqrt{3}+2 \sqrt{2}}$

Write the following in decimal form and state what kind of decimal expansion each has:
$\frac{2}{11}$

Find three rational numbers between $\frac{1}{4}$ and $\frac{1}{5}$.

Prove that $(1^{3}+2^{3}+3^{3}+4^{3}+5^{3})^{\frac{1}{2}} = (1^{3}+2^{3}+3^{3}+4^{3})^{\frac{1}{2}} + (5^{3})^{\frac{1}{3}}$.

Show that $0.142857142857... = 0.\overline{142857} = \frac{1}{7}$.