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

\( \frac{18\sqrt{14}}{9\sqrt{7}} \)
\( \frac{18}{9} \) \( \sqrt{\frac{14}{7}} \)
2 \( \sqrt{2} \)

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

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:

\( \sqrt{\frac{36}{16}} \)
\( \frac{\sqrt{36}}{\sqrt{16}} \)
\( \frac{\sqrt{6^2}}{\sqrt{4^2}} \)
\( \frac{6}{4} \)
1\(\frac{1}{2}\)

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.1km + 30.6km + 10.1km
total distance = 40.8km

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

vans = \( \frac{70}{11} \) = 6\(\frac{4}{11}\)

So, it will take 6 full vans and one partially full van to transport the entire team making a total of 7 vans.