| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.31 |
| Score | 0% | 66% |
What is \( 7 \)\( \sqrt{28} \) + \( 6 \)\( \sqrt{7} \)
| 42\( \sqrt{196} \) | |
| 20\( \sqrt{7} \) | |
| 13\( \sqrt{4} \) | |
| 42\( \sqrt{7} \) |
To add these radicals together their radicands must be the same:
7\( \sqrt{28} \) + 6\( \sqrt{7} \)
7\( \sqrt{4 \times 7} \) + 6\( \sqrt{7} \)
7\( \sqrt{2^2 \times 7} \) + 6\( \sqrt{7} \)
(7)(2)\( \sqrt{7} \) + 6\( \sqrt{7} \)
14\( \sqrt{7} \) + 6\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
14\( \sqrt{7} \) + 6\( \sqrt{7} \)What is \( \frac{4}{5} \) x \( \frac{2}{8} \)?
| \(\frac{8}{45}\) | |
| \(\frac{4}{15}\) | |
| \(\frac{1}{5}\) | |
| 1\(\frac{3}{5}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{5} \) x \( \frac{2}{8} \) = \( \frac{4 x 2}{5 x 8} \) = \( \frac{8}{40} \) = \(\frac{1}{5}\)
Simplify \( \sqrt{20} \)
| 6\( \sqrt{10} \) | |
| 4\( \sqrt{10} \) | |
| 2\( \sqrt{5} \) | |
| 9\( \sqrt{10} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{20} \)
\( \sqrt{4 \times 5} \)
\( \sqrt{2^2 \times 5} \)
2\( \sqrt{5} \)
What is 7a4 x 6a2?
| 42a2 | |
| 13a2 | |
| 42a6 | |
| 42a4 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
7a4 x 6a2
(7 x 6)a(4 + 2)
42a6
If a car travels 55 miles in 1 hour, what is the average speed?
| 15 mph | |
| 50 mph | |
| 25 mph | |
| 55 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)