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

9\( \sqrt{112} \) - 3\( \sqrt{7} \)
9\( \sqrt{16 \times 7} \) - 3\( \sqrt{7} \)
9\( \sqrt{4^2 \times 7} \) - 3\( \sqrt{7} \)
(9)(4)\( \sqrt{7} \) - 3\( \sqrt{7} \)
36\( \sqrt{7} \) - 3\( \sqrt{7} \)

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

To fill a 9 gallon tank exactly halfway you'll need 4\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{4\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 3

The number of students taking German or Spanish is 15 + 7 = 22. Of that group of 22, 3 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 22 - 3 = 19 who are taking at least one language. 28 - 19 = 9 students who are not taking either language.

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

6\( \sqrt{12} \) + 5\( \sqrt{3} \)
6\( \sqrt{4 \times 3} \) + 5\( \sqrt{3} \)
6\( \sqrt{2^2 \times 3} \) + 5\( \sqrt{3} \)
(6)(2)\( \sqrt{3} \) + 5\( \sqrt{3} \)
12\( \sqrt{3} \) + 5\( \sqrt{3} \)

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

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 4 workers at the company now and that's enough to staff 2 crews so there are \( \frac{4}{2} \) = 2 workers on a crew. 7 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 7 x 2 = 14 total workers to staff the crews during the busy season. The company already employs 4 workers so they need to add 14 - 4 = 10 new staff for the busy season.