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

6\( \sqrt{112} \) - 6\( \sqrt{7} \)
6\( \sqrt{16 \times 7} \) - 6\( \sqrt{7} \)
6\( \sqrt{4^2 \times 7} \) - 6\( \sqrt{7} \)
(6)(4)\( \sqrt{7} \) - 6\( \sqrt{7} \)
24\( \sqrt{7} \) - 6\( \sqrt{7} \)

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

If a single cook can bake 5 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 5 x 3 = 15 large cakes during that time. 23 large cakes are needed for the party so \( \frac{23}{15} \) = 1\(\frac{8}{15}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 20 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 20 x 3 = 60 small cakes during that time. 480 small cakes are needed for the party so \( \frac{480}{60} \) = 8 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 + 8 = 10 cooks.

You have 9 out of the total of 150 raffle tickets sold so you have a (\( \frac{9}{150} \)) x 100 = \( \frac{9 \times 100}{150} \) = \( \frac{900}{150} \) = 6% chance to win the raffle.

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

2\( \sqrt{6} \) x 4\( \sqrt{5} \)
(2 x 4)\( \sqrt{6 \times 5} \)
8\( \sqrt{30} \)

There are 2 3-passenger taxis available so that's 2 x 3 = 6 total seats. There are 7 people needing transportation leaving 7 - 6 = 1 who will have to find other transportation.