| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.08 |
| Score | 0% | 62% |
What is \( 7 \)\( \sqrt{28} \) - \( 8 \)\( \sqrt{7} \)
| -1\( \sqrt{7} \) | |
| -1\( \sqrt{196} \) | |
| 56\( \sqrt{196} \) | |
| 6\( \sqrt{7} \) |
To subtract these radicals together their radicands must be the same:
7\( \sqrt{28} \) - 8\( \sqrt{7} \)
7\( \sqrt{4 \times 7} \) - 8\( \sqrt{7} \)
7\( \sqrt{2^2 \times 7} \) - 8\( \sqrt{7} \)
(7)(2)\( \sqrt{7} \) - 8\( \sqrt{7} \)
14\( \sqrt{7} \) - 8\( \sqrt{7} \)
Now that the radicands are identical, you can subtract them:
14\( \sqrt{7} \) - 8\( \sqrt{7} \)What is the next number in this sequence: 1, 4, 7, 10, 13, __________ ?
| 10 | |
| 20 | |
| 16 | |
| 11 |
The equation for this sequence is:
an = an-1 + 3
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 3
a6 = 13 + 3
a6 = 16
What is (c2)5?
| 2c5 | |
| c10 | |
| 5c2 | |
| c7 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(c2)5Simplify \( \sqrt{28} \)
| 2\( \sqrt{7} \) | |
| 7\( \sqrt{14} \) | |
| 3\( \sqrt{7} \) | |
| 9\( \sqrt{14} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{28} \)
\( \sqrt{4 \times 7} \)
\( \sqrt{2^2 \times 7} \)
2\( \sqrt{7} \)
What is \( 8 \)\( \sqrt{50} \) + \( 2 \)\( \sqrt{2} \)
| 10\( \sqrt{50} \) | |
| 42\( \sqrt{2} \) | |
| 16\( \sqrt{2} \) | |
| 10\( \sqrt{2} \) |
To add these radicals together their radicands must be the same:
8\( \sqrt{50} \) + 2\( \sqrt{2} \)
8\( \sqrt{25 \times 2} \) + 2\( \sqrt{2} \)
8\( \sqrt{5^2 \times 2} \) + 2\( \sqrt{2} \)
(8)(5)\( \sqrt{2} \) + 2\( \sqrt{2} \)
40\( \sqrt{2} \) + 2\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
40\( \sqrt{2} \) + 2\( \sqrt{2} \)