| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.79 |
| Score | 0% | 56% |
What is \( 9 \)\( \sqrt{75} \) + \( 5 \)\( \sqrt{3} \)
| 14\( \sqrt{225} \) | |
| 14\( \sqrt{3} \) | |
| 45\( \sqrt{75} \) | |
| 50\( \sqrt{3} \) |
To add these radicals together their radicands must be the same:
9\( \sqrt{75} \) + 5\( \sqrt{3} \)
9\( \sqrt{25 \times 3} \) + 5\( \sqrt{3} \)
9\( \sqrt{5^2 \times 3} \) + 5\( \sqrt{3} \)
(9)(5)\( \sqrt{3} \) + 5\( \sqrt{3} \)
45\( \sqrt{3} \) + 5\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
45\( \sqrt{3} \) + 5\( \sqrt{3} \)Which of the following is not an integer?
-1 |
|
0 |
|
1 |
|
\({1 \over 2}\) |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
What is 3\( \sqrt{4} \) x 2\( \sqrt{3} \)?
| 5\( \sqrt{12} \) | |
| 6\( \sqrt{3} \) | |
| 5\( \sqrt{3} \) | |
| 12\( \sqrt{3} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
3\( \sqrt{4} \) x 2\( \sqrt{3} \)
(3 x 2)\( \sqrt{4 \times 3} \)
6\( \sqrt{12} \)
Now we need to simplify the radical:
6\( \sqrt{12} \)
6\( \sqrt{3 \times 4} \)
6\( \sqrt{3 \times 2^2} \)
(6)(2)\( \sqrt{3} \)
12\( \sqrt{3} \)
Solve 3 + (5 + 4) ÷ 2 x 4 - 32
| \(\frac{2}{3}\) | |
| 12 | |
| 3\(\frac{1}{2}\) | |
| 1 |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
3 + (5 + 4) ÷ 2 x 4 - 32
P: 3 + (9) ÷ 2 x 4 - 32
E: 3 + 9 ÷ 2 x 4 - 9
MD: 3 + \( \frac{9}{2} \) x 4 - 9
MD: 3 + \( \frac{36}{2} \) - 9
AS: \( \frac{6}{2} \) + \( \frac{36}{2} \) - 9
AS: \( \frac{42}{2} \) - 9
AS: \( \frac{42 - 18}{2} \)
\( \frac{24}{2} \)
12
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 50% off." If Frank buys two shirts, each with a regular price of $14, how much money will he save?
| $4.20 | |
| $2.10 | |
| $3.50 | |
| $7.00 |
By buying two shirts, Frank will save $14 x \( \frac{50}{100} \) = \( \frac{$14 x 50}{100} \) = \( \frac{$700}{100} \) = $7.00 on the second shirt.