A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

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

2\( \sqrt{4} \) x 6\( \sqrt{7} \)
(2 x 6)\( \sqrt{4 \times 7} \)
12\( \sqrt{28} \)

Now we need to simplify the radical:

12\( \sqrt{28} \)
12\( \sqrt{7 \times 4} \)
12\( \sqrt{7 \times 2^2} \)
(12)(2)\( \sqrt{7} \)
24\( \sqrt{7} \)

If a single cook can bake 2 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 2 x 4 = 8 large cakes during that time. 21 large cakes are needed for the party so \( \frac{21}{8} \) = 2\(\frac{5}{8}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 17 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 17 x 4 = 68 small cakes during that time. 190 small cakes are needed for the party so \( \frac{190}{68} \) = 2\(\frac{27}{34}\) 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 3 + 3 = 6 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 add these radicals together their radicands must be the same:

6\( \sqrt{28} \) + 8\( \sqrt{7} \)
6\( \sqrt{4 \times 7} \) + 8\( \sqrt{7} \)
6\( \sqrt{2^2 \times 7} \) + 8\( \sqrt{7} \)
(6)(2)\( \sqrt{7} \) + 8\( \sqrt{7} \)
12\( \sqrt{7} \) + 8\( \sqrt{7} \)

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