The number of students taking German or Spanish is 12 + 7 = 19. Of that group of 19, 5 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 19 - 5 = 14 who are taking at least one language. 26 - 14 = 12 students who are not taking either language.

To simplify a radical, factor out the perfect squares:

\( \sqrt{20} \)
\( \sqrt{4 \times 5} \)
\( \sqrt{2^2 \times 5} \)
2\( \sqrt{5} \)

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

\( \frac{11 + 7 + 12 + 6}{4} \) = \( \frac{36}{4} \) = 9

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

2\( \sqrt{5} \) x 4\( \sqrt{8} \)
(2 x 4)\( \sqrt{5 \times 8} \)
8\( \sqrt{40} \)

Now we need to simplify the radical:

8\( \sqrt{40} \)
8\( \sqrt{10 \times 4} \)
8\( \sqrt{10 \times 2^2} \)
(8)(2)\( \sqrt{10} \)
16\( \sqrt{10} \)

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

8\( \sqrt{112} \) - 3\( \sqrt{7} \)
8\( \sqrt{16 \times 7} \) - 3\( \sqrt{7} \)
8\( \sqrt{4^2 \times 7} \) - 3\( \sqrt{7} \)
(8)(4)\( \sqrt{7} \) - 3\( \sqrt{7} \)
32\( \sqrt{7} \) - 3\( \sqrt{7} \)

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