| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.15 |
| Score | 0% | 63% |
Simplify \( \sqrt{8} \)
| 2\( \sqrt{2} \) | |
| 9\( \sqrt{2} \) | |
| 6\( \sqrt{4} \) | |
| 5\( \sqrt{2} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{8} \)
\( \sqrt{4 \times 2} \)
\( \sqrt{2^2 \times 2} \)
2\( \sqrt{2} \)
The total water usage for a city is 20,000 gallons each day. Of that total, 35% is for personal use and 48% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 2,600 | |
| 850 | |
| 13,200 | |
| 1,200 |
48% of the water consumption is industrial use and 35% is personal use so (48% - 35%) = 13% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{13}{100} \) x 20,000 gallons = 2,600 gallons.
What is \( \frac{4}{8} \) ÷ \( \frac{4}{6} \)?
| \(\frac{1}{14}\) | |
| \(\frac{1}{6}\) | |
| \(\frac{3}{4}\) | |
| \(\frac{1}{15}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{8} \) ÷ \( \frac{4}{6} \) = \( \frac{4}{8} \) x \( \frac{6}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{8} \) x \( \frac{6}{4} \) = \( \frac{4 x 6}{8 x 4} \) = \( \frac{24}{32} \) = \(\frac{3}{4}\)
What is \( \frac{35\sqrt{15}}{7\sqrt{3}} \)?
| \(\frac{1}{5}\) \( \sqrt{\frac{1}{5}} \) | |
| 5 \( \sqrt{\frac{1}{5}} \) | |
| \(\frac{1}{5}\) \( \sqrt{5} \) | |
| 5 \( \sqrt{5} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{35\sqrt{15}}{7\sqrt{3}} \)
\( \frac{35}{7} \) \( \sqrt{\frac{15}{3}} \)
5 \( \sqrt{5} \)
The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
|
greatest common factor |
|
least common factor |
|
least common multiple |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.