| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.92 |
| Score | 0% | 58% |
What is \( \frac{6\sqrt{12}}{2\sqrt{4}} \)?
| 3 \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{3}} \) | |
| 3 \( \sqrt{\frac{1}{3}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{6\sqrt{12}}{2\sqrt{4}} \)
\( \frac{6}{2} \) \( \sqrt{\frac{12}{4}} \)
3 \( \sqrt{3} \)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 25% off." If Monty buys two shirts, each with a regular price of $50, how much will he pay for both shirts?
| $67.50 | |
| $87.50 | |
| $65.00 | |
| $37.50 |
By buying two shirts, Monty will save $50 x \( \frac{25}{100} \) = \( \frac{$50 x 25}{100} \) = \( \frac{$1250}{100} \) = $12.50 on the second shirt.
So, his total cost will be
$50.00 + ($50.00 - $12.50)
$50.00 + $37.50
$87.50
A tiger in a zoo has consumed 108 pounds of food in 9 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 156 pounds?
| 4 | |
| 1 | |
| 5 | |
| 6 |
If the tiger has consumed 108 pounds of food in 9 days that's \( \frac{108}{9} \) = 12 pounds of food per day. The tiger needs to consume 156 - 108 = 48 more pounds of food to reach 156 pounds total. At 12 pounds of food per day that's \( \frac{48}{12} \) = 4 more days.
What is \( \sqrt{\frac{81}{25}} \)?
| 1\(\frac{4}{5}\) | |
| 2\(\frac{1}{3}\) | |
| 2 | |
| \(\frac{2}{3}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{81}{25}} \)
\( \frac{\sqrt{81}}{\sqrt{25}} \)
\( \frac{\sqrt{9^2}}{\sqrt{5^2}} \)
\( \frac{9}{5} \)
1\(\frac{4}{5}\)
What is \( 2 \)\( \sqrt{75} \) - \( 9 \)\( \sqrt{3} \)
| 18\( \sqrt{75} \) | |
| 18\( \sqrt{3} \) | |
| \( \sqrt{3} \) | |
| -7\( \sqrt{-16} \) |
To subtract these radicals together their radicands must be the same:
2\( \sqrt{75} \) - 9\( \sqrt{3} \)
2\( \sqrt{25 \times 3} \) - 9\( \sqrt{3} \)
2\( \sqrt{5^2 \times 3} \) - 9\( \sqrt{3} \)
(2)(5)\( \sqrt{3} \) - 9\( \sqrt{3} \)
10\( \sqrt{3} \) - 9\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
10\( \sqrt{3} \) - 9\( \sqrt{3} \)