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

4\( \sqrt{27} \) + 8\( \sqrt{3} \)
4\( \sqrt{9 \times 3} \) + 8\( \sqrt{3} \)
4\( \sqrt{3^2 \times 3} \) + 8\( \sqrt{3} \)
(4)(3)\( \sqrt{3} \) + 8\( \sqrt{3} \)
12\( \sqrt{3} \) + 8\( \sqrt{3} \)

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

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-3c³ - 5c³
(-3 - 5)c³
-8c³

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.1km + 40.6km + 8.0km
total distance = 48.7km

Christine scored 89% on the test meaning she earned 89% of the possible points on the test. There were 280 possible points on the test so she earned 280 x 0.89 = 248 points. Each question is worth 4 points so she got \( \frac{248}{4} \) = 62 questions right.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{7} \) x \( \frac{2}{5} \) = \( \frac{2 x 2}{7 x 5} \) = \( \frac{4}{35} \) = \(\frac{4}{35}\)