| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.08 |
| Score | 0% | 62% |
What is 8\( \sqrt{5} \) x 5\( \sqrt{9} \)?
| 40\( \sqrt{14} \) | |
| 13\( \sqrt{5} \) | |
| 120\( \sqrt{5} \) | |
| 13\( \sqrt{9} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
8\( \sqrt{5} \) x 5\( \sqrt{9} \)
(8 x 5)\( \sqrt{5 \times 9} \)
40\( \sqrt{45} \)
Now we need to simplify the radical:
40\( \sqrt{45} \)
40\( \sqrt{5 \times 9} \)
40\( \sqrt{5 \times 3^2} \)
(40)(3)\( \sqrt{5} \)
120\( \sqrt{5} \)
What is \( 8 \)\( \sqrt{175} \) - \( 9 \)\( \sqrt{7} \)
| 31\( \sqrt{7} \) | |
| -1\( \sqrt{25} \) | |
| -1\( \sqrt{1225} \) | |
| 72\( \sqrt{1225} \) |
To subtract these radicals together their radicands must be the same:
8\( \sqrt{175} \) - 9\( \sqrt{7} \)
8\( \sqrt{25 \times 7} \) - 9\( \sqrt{7} \)
8\( \sqrt{5^2 \times 7} \) - 9\( \sqrt{7} \)
(8)(5)\( \sqrt{7} \) - 9\( \sqrt{7} \)
40\( \sqrt{7} \) - 9\( \sqrt{7} \)
Now that the radicands are identical, you can subtract them:
40\( \sqrt{7} \) - 9\( \sqrt{7} \)What is \( \frac{21\sqrt{6}}{7\sqrt{2}} \)?
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{3}} \) | |
| \(\frac{1}{3}\) \( \sqrt{3} \) | |
| 3 \( \sqrt{3} \) | |
| 3 \( \sqrt{\frac{1}{3}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{21\sqrt{6}}{7\sqrt{2}} \)
\( \frac{21}{7} \) \( \sqrt{\frac{6}{2}} \)
3 \( \sqrt{3} \)
Charlie loaned Roger $1,500 at an annual interest rate of 3%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $36 | |
| $1 | |
| $35 | |
| $45 |
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 $1,500
i = 0.03 x $1,500
i = $45
Which of the following is a mixed number?
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({7 \over 5} \) |
|
\({5 \over 7} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.