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

2\( \sqrt{125} \) + 2\( \sqrt{5} \)
2\( \sqrt{25 \times 5} \) + 2\( \sqrt{5} \)
2\( \sqrt{5^2 \times 5} \) + 2\( \sqrt{5} \)
(2)(5)\( \sqrt{5} \) + 2\( \sqrt{5} \)
10\( \sqrt{5} \) + 2\( \sqrt{5} \)

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

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 + 40.1km + 12.4km
total distance = 52.6km

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{z^5}{2z^4} \)
\( \frac{1}{2} \) z^{(5 - 4)}
\(\frac{1}{2}\)z

If 67% of the town's 44,000 voters cast ballots the number of votes cast is:

(\( \frac{67}{100} \)) x 44,000 = \( \frac{2,948,000}{100} \) = 29,480

The mayor got 69% of the votes cast which is:

(\( \frac{69}{100} \)) x 29,480 = \( \frac{2,034,120}{100} \) = 20,341 votes.