| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.24 |
| Score | 0% | 65% |
If a car travels 150 miles in 3 hours, what is the average speed?
| 55 mph | |
| 15 mph | |
| 75 mph | |
| 50 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Simplify \( \sqrt{8} \)
| 2\( \sqrt{2} \) | |
| 7\( \sqrt{4} \) | |
| 4\( \sqrt{4} \) | |
| 5\( \sqrt{4} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{8} \)
\( \sqrt{4 \times 2} \)
\( \sqrt{2^2 \times 2} \)
2\( \sqrt{2} \)
What is 4a4 + 8a4?
| 12a8 | |
| 12a4 | |
| 12a16 | |
| 12a-8 |
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:
4a4 + 8a4
(4 + 8)a4
12a4
What is 4\( \sqrt{3} \) x 7\( \sqrt{9} \)?
| 11\( \sqrt{27} \) | |
| 28\( \sqrt{3} \) | |
| 28\( \sqrt{12} \) | |
| 84\( \sqrt{3} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
4\( \sqrt{3} \) x 7\( \sqrt{9} \)
(4 x 7)\( \sqrt{3 \times 9} \)
28\( \sqrt{27} \)
Now we need to simplify the radical:
28\( \sqrt{27} \)
28\( \sqrt{3 \times 9} \)
28\( \sqrt{3 \times 3^2} \)
(28)(3)\( \sqrt{3} \)
84\( \sqrt{3} \)
What is \( \sqrt{\frac{81}{16}} \)?
| 1\(\frac{3}{5}\) | |
| 3 | |
| 1\(\frac{4}{5}\) | |
| 2\(\frac{1}{4}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{81}{16}} \)
\( \frac{\sqrt{81}}{\sqrt{16}} \)
\( \frac{\sqrt{9^2}}{\sqrt{4^2}} \)
\( \frac{9}{4} \)
2\(\frac{1}{4}\)