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

8\( \sqrt{8} \) x 8\( \sqrt{6} \)
(8 x 8)\( \sqrt{8 \times 6} \)
64\( \sqrt{48} \)

Now we need to simplify the radical:

64\( \sqrt{48} \)
64\( \sqrt{3 \times 16} \)
64\( \sqrt{3 \times 4^2} \)
(64)(4)\( \sqrt{3} \)
256\( \sqrt{3} \)

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

vans = \( \frac{88}{12} \) = 7\(\frac{1}{3}\)

So, it will take 7 full vans and one partially full van to transport the entire team making a total of 8 vans.

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:

\( \frac{2!}{5!} \)
\( \frac{2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4 \times 3} \)
\( \frac{1}{60} \)

To subtract these radicals together their radicands must be the same:

3\( \sqrt{27} \) - 5\( \sqrt{3} \)
3\( \sqrt{9 \times 3} \) - 5\( \sqrt{3} \)
3\( \sqrt{3^2 \times 3} \) - 5\( \sqrt{3} \)
(3)(3)\( \sqrt{3} \) - 5\( \sqrt{3} \)
9\( \sqrt{3} \) - 5\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them:

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).