To simplify a radical, factor out the perfect squares:

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

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:

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

The number of students taking German or Spanish is 11 + 12 = 23. Of that group of 23, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 23 - 2 = 21 who are taking at least one language. 29 - 21 = 8 students who are not taking either language.

The amount of flour you need is (2\(\frac{5}{8}\) - 1\(\frac{1}{2}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{21}{8} \) - \( \frac{12}{8} \)) cups
\( \frac{9}{8} \) cups
1\(\frac{1}{8}\) cups

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

2 + (3 + 5) ÷ 3 x 2 - 4²
P: 2 + (8) ÷ 3 x 2 - 4²
E: 2 + 8 ÷ 3 x 2 - 16
MD: 2 + \( \frac{8}{3} \) x 2 - 16
MD: 2 + \( \frac{16}{3} \) - 16
AS: \( \frac{6}{3} \) + \( \frac{16}{3} \) - 16
AS: \( \frac{22}{3} \) - 16
AS: \( \frac{22 - 48}{3} \)
\( \frac{-26}{3} \)
-8\(\frac{2}{3}\)