| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.83 |
| Score | 0% | 57% |
What is 8\( \sqrt{2} \) x 5\( \sqrt{2} \)?
| 80 | |
| 40\( \sqrt{2} \) | |
| 40\( \sqrt{4} \) | |
| 13\( \sqrt{4} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
8\( \sqrt{2} \) x 5\( \sqrt{2} \)
(8 x 5)\( \sqrt{2 \times 2} \)
40\( \sqrt{4} \)
Now we need to simplify the radical:
40\( \sqrt{4} \)
40\( \sqrt{2^2} \)
(40)(2)
80
How many 10-passenger vans will it take to drive all 33 members of the football team to an away game?
| 4 vans | |
| 6 vans | |
| 7 vans | |
| 9 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{33}{10} \) = 3\(\frac{3}{10}\)
So, it will take 3 full vans and one partially full van to transport the entire team making a total of 4 vans.
Ezra loaned Monty $1,400 at an annual interest rate of 8%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $21 | |
| $18 | |
| $112 | |
| $6 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $1,400
i = 0.08 x $1,400
i = $112
| 4.0 | |
| 6.3 | |
| 1 | |
| 3.0 |
1
What is \( 4 \)\( \sqrt{75} \) + \( 3 \)\( \sqrt{3} \)
| 7\( \sqrt{3} \) | |
| 12\( \sqrt{75} \) | |
| 12\( \sqrt{225} \) | |
| 23\( \sqrt{3} \) |
To add these radicals together their radicands must be the same:
4\( \sqrt{75} \) + 3\( \sqrt{3} \)
4\( \sqrt{25 \times 3} \) + 3\( \sqrt{3} \)
4\( \sqrt{5^2 \times 3} \) + 3\( \sqrt{3} \)
(4)(5)\( \sqrt{3} \) + 3\( \sqrt{3} \)
20\( \sqrt{3} \) + 3\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
20\( \sqrt{3} \) + 3\( \sqrt{3} \)