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

4\( \sqrt{4} \) x 8\( \sqrt{4} \)
(4 x 8)\( \sqrt{4 \times 4} \)
32\( \sqrt{16} \)

Now we need to simplify the radical:

32\( \sqrt{16} \)
32\( \sqrt{4^2} \)
(32)(4)
128

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

8\( \sqrt{175} \) + 4\( \sqrt{7} \)
8\( \sqrt{25 \times 7} \) + 4\( \sqrt{7} \)
8\( \sqrt{5^2 \times 7} \) + 4\( \sqrt{7} \)
(8)(5)\( \sqrt{7} \) + 4\( \sqrt{7} \)
40\( \sqrt{7} \) + 4\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (3 + 4) ÷ 4 x 3 - 3²
P: 2 + (7) ÷ 4 x 3 - 3²
E: 2 + 7 ÷ 4 x 3 - 9
MD: 2 + \( \frac{7}{4} \) x 3 - 9
MD: 2 + \( \frac{21}{4} \) - 9
AS: \( \frac{8}{4} \) + \( \frac{21}{4} \) - 9
AS: \( \frac{29}{4} \) - 9
AS: \( \frac{29 - 36}{4} \)
\( \frac{-7}{4} \)
-1\(\frac{3}{4}\)

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{14 + 6 + 11 + 9}{4} \) = \( \frac{40}{4} \) = 10