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

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

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

If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 23 large cakes are needed for the party so \( \frac{23}{12} \) = 1\(\frac{11}{12}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 13 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 13 x 4 = 52 small cakes during that time. 140 small cakes are needed for the party so \( \frac{140}{52} \) = 2\(\frac{9}{13}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 3 = 5 cooks.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

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

8\( \sqrt{32} \) + 5\( \sqrt{2} \)
8\( \sqrt{16 \times 2} \) + 5\( \sqrt{2} \)
8\( \sqrt{4^2 \times 2} \) + 5\( \sqrt{2} \)
(8)(4)\( \sqrt{2} \) + 5\( \sqrt{2} \)
32\( \sqrt{2} \) + 5\( \sqrt{2} \)

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

To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{10 \text{ gallons}}{2 \text{ gallons}} \) = 5