| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
Simplify \( \sqrt{27} \)
| 4\( \sqrt{6} \) | |
| 9\( \sqrt{3} \) | |
| 3\( \sqrt{3} \) | |
| 6\( \sqrt{3} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{27} \)
\( \sqrt{9 \times 3} \)
\( \sqrt{3^2 \times 3} \)
3\( \sqrt{3} \)
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 50,000 seats in a stadium are filled, how many home fans are in attendance?
| 41,667 | |
| 30,000 | |
| 24,000 | |
| 20,667 |
A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:
50,000 fans x \( \frac{5}{6} \) = \( \frac{250000}{6} \) = 41,667 fans.
What is \( \frac{14\sqrt{36}}{2\sqrt{9}} \)?
| 7 \( \sqrt{\frac{1}{4}} \) | |
| 7 \( \sqrt{4} \) | |
| \(\frac{1}{7}\) \( \sqrt{\frac{1}{4}} \) | |
| \(\frac{1}{7}\) \( \sqrt{4} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{14\sqrt{36}}{2\sqrt{9}} \)
\( \frac{14}{2} \) \( \sqrt{\frac{36}{9}} \)
7 \( \sqrt{4} \)
Which of the following is not a prime number?
2 |
|
9 |
|
7 |
|
5 |
A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.
What is the least common multiple of 3 and 5?
| 15 | |
| 6 | |
| 4 | |
| 5 |
The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 have in common.