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

vans = \( \frac{65}{10} \) = 6\(\frac{1}{2}\)

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

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

2\( \sqrt{8} \) x 3\( \sqrt{8} \)
(2 x 3)\( \sqrt{8 \times 8} \)
6\( \sqrt{64} \)

Now we need to simplify the radical:

6\( \sqrt{64} \)
6\( \sqrt{8^2} \)
(6)(8)
48

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 4}{6 x 4} \) - \( \frac{9 x 3}{8 x 3} \)

\( \frac{16}{24} \) - \( \frac{27}{24} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{16 - 27}{24} \) = \( \frac{-11}{24} \) = -\(\frac{11}{24}\)

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.