To add these radicals together their radicands must be the same:

4\( \sqrt{18} \) + 8\( \sqrt{2} \)
4\( \sqrt{9 \times 2} \) + 8\( \sqrt{2} \)
4\( \sqrt{3^2 \times 2} \) + 8\( \sqrt{2} \)
(4)(3)\( \sqrt{2} \) + 8\( \sqrt{2} \)
12\( \sqrt{2} \) + 8\( \sqrt{2} \)

Now that the radicands are identical, you can add them together:

Betty scored 83% on the test meaning she earned 83% of the possible points on the test. There were 90 possible points on the test so she earned 90 x 0.83 = 75 points. Each question is worth 3 points so she got \( \frac{75}{3} \) = 25 questions right.

To fill a 15 gallon tank exactly halfway you'll need 7\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{7\frac{1}{2} \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 3

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{56\sqrt{35}}{8\sqrt{7}} \)
\( \frac{56}{8} \) \( \sqrt{\frac{35}{7}} \)
7 \( \sqrt{5} \)

The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 have in common.