| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.27 |
| Score | 0% | 65% |
Simplify \( \sqrt{20} \)
| 6\( \sqrt{5} \) | |
| 2\( \sqrt{5} \) | |
| 4\( \sqrt{5} \) | |
| 8\( \sqrt{10} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{20} \)
\( \sqrt{4 \times 5} \)
\( \sqrt{2^2 \times 5} \)
2\( \sqrt{5} \)
Find the average of the following numbers: 14, 8, 15, 7.
| 8 | |
| 11 | |
| 14 | |
| 9 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{14 + 8 + 15 + 7}{4} \) = \( \frac{44}{4} \) = 11
If a car travels 45 miles in 1 hour, what is the average speed?
| 70 mph | |
| 30 mph | |
| 45 mph | |
| 15 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)A triathlon course includes a 500m swim, a 30.2km bike ride, and a 9.2km run. What is the total length of the race course?
| 39.9km | |
| 32.8km | |
| 58km | |
| 41.5km |
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 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.5km + 30.2km + 9.2km
total distance = 39.9km
What is \( 7 \)\( \sqrt{125} \) + \( 7 \)\( \sqrt{5} \)
| 49\( \sqrt{625} \) | |
| 49\( \sqrt{125} \) | |
| 14\( \sqrt{625} \) | |
| 42\( \sqrt{5} \) |
To add these radicals together their radicands must be the same:
7\( \sqrt{125} \) + 7\( \sqrt{5} \)
7\( \sqrt{25 \times 5} \) + 7\( \sqrt{5} \)
7\( \sqrt{5^2 \times 5} \) + 7\( \sqrt{5} \)
(7)(5)\( \sqrt{5} \) + 7\( \sqrt{5} \)
35\( \sqrt{5} \) + 7\( \sqrt{5} \)
Now that the radicands are identical, you can add them together:
35\( \sqrt{5} \) + 7\( \sqrt{5} \)