| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.28 |
| Score | 0% | 66% |
What is \( \frac{12\sqrt{36}}{4\sqrt{9}} \)?
| 3 \( \sqrt{4} \) | |
| 4 \( \sqrt{3} \) | |
| 4 \( \sqrt{\frac{1}{3}} \) | |
| \(\frac{1}{3}\) \( \sqrt{4} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{12\sqrt{36}}{4\sqrt{9}} \)
\( \frac{12}{4} \) \( \sqrt{\frac{36}{9}} \)
3 \( \sqrt{4} \)
In a class of 37 students, 9 are taking German and 15 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 13 | |
| 15 | |
| 18 | |
| 26 |
The number of students taking German or Spanish is 9 + 15 = 24. Of that group of 24, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 24 - 2 = 22 who are taking at least one language. 37 - 22 = 15 students who are not taking either language.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
PEDMAS |
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associative |
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distributive |
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commutative |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
Simplify \( \sqrt{18} \)
| 3\( \sqrt{2} \) | |
| 7\( \sqrt{4} \) | |
| 6\( \sqrt{4} \) | |
| 5\( \sqrt{2} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{18} \)
\( \sqrt{9 \times 2} \)
\( \sqrt{3^2 \times 2} \)
3\( \sqrt{2} \)
What is the least common multiple of 2 and 8?
| 16 | |
| 8 | |
| 14 | |
| 4 |
The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 have in common.