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

6\( \sqrt{2} \) x 2\( \sqrt{6} \)
(6 x 2)\( \sqrt{2 \times 6} \)
12\( \sqrt{12} \)

Now we need to simplify the radical:

12\( \sqrt{12} \)
12\( \sqrt{3 \times 4} \)
12\( \sqrt{3 \times 2^2} \)
(12)(2)\( \sqrt{3} \)
24\( \sqrt{3} \)

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{7 + 5 + 8 + 4}{4} \) = \( \frac{24}{4} \) = 6

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

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{135mi}{15mph} \)
9 hours

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

4\( \sqrt{75} \) + 8\( \sqrt{3} \)
4\( \sqrt{25 \times 3} \) + 8\( \sqrt{3} \)
4\( \sqrt{5^2 \times 3} \) + 8\( \sqrt{3} \)
(4)(5)\( \sqrt{3} \) + 8\( \sqrt{3} \)
20\( \sqrt{3} \) + 8\( \sqrt{3} \)

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 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.4km + 30.5km + 5.9km
total distance = 36.8km