After rationalizing the denominator of $\frac{7}{3 \sqrt{3}-2 \sqrt{2}},$ we get the denominator as

Fill in the blanks to make the following statement true: $\sqrt{2} \cdot \sqrt{3} \cdot \sqrt{6} = \dots$

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 $\sqrt{5} = 2.236$.
$\frac{4}{3 \sqrt{3}-2 \sqrt{2}} + \frac{3}{3 \sqrt{3}+2 \sqrt{2}}$

Represent $\sqrt{10}$ on the number line.

Write the following in decimal form and state what kind of decimal expansion each has:
$\frac{5}{13}$

If $\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{6}}=a+b \sqrt{30}$,find the value of $a$ and $b$.