Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{57}{13} \) = 4\(\frac{5}{13}\)

So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.

If the tiger has consumed 90 pounds of food in 6 days that's \( \frac{90}{6} \) = 15 pounds of food per day. The tiger needs to consume 135 - 90 = 45 more pounds of food to reach 135 pounds total. At 15 pounds of food per day that's \( \frac{45}{15} \) = 3 more days.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{25}{81}} \)
\( \frac{\sqrt{25}}{\sqrt{81}} \)
\( \frac{\sqrt{5^2}}{\sqrt{9^2}} \)
\(\frac{5}{9}\)

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{14\sqrt{40}}{7\sqrt{8}} \)
\( \frac{14}{7} \) \( \sqrt{\frac{40}{8}} \)
2 \( \sqrt{5} \)

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{4!}{2!} \)
\( \frac{4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{4 \times 3}{1} \)
\( 4 \times 3 \)
12