The factors of 44 are [1, 2, 4, 11, 22, 44] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 the greatest factor 44 and 68 have in common.

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

5\( \sqrt{125} \) + 3\( \sqrt{5} \)
5\( \sqrt{25 \times 5} \) + 3\( \sqrt{5} \)
5\( \sqrt{5^2 \times 5} \) + 3\( \sqrt{5} \)
(5)(5)\( \sqrt{5} \) + 3\( \sqrt{5} \)
25\( \sqrt{5} \) + 3\( \sqrt{5} \)

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

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.1km + 30.9km + 6.4km
total distance = 37.4km

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

5x³ + 7x³
(5 + 7)x³
12x³

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 15 workers at the company now and that's enough to staff 5 crews so there are \( \frac{15}{5} \) = 3 workers on a crew. 7 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 7 x 3 = 21 total workers to staff the crews during the busy season. The company already employs 15 workers so they need to add 21 - 15 = 6 new staff for the busy season.