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

3\( \sqrt{125} \) - 5\( \sqrt{5} \)
3\( \sqrt{25 \times 5} \) - 5\( \sqrt{5} \)
3\( \sqrt{5^2 \times 5} \) - 5\( \sqrt{5} \)
(3)(5)\( \sqrt{5} \) - 5\( \sqrt{5} \)
15\( \sqrt{5} \) - 5\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

If 30% of the town's 28,000 voters cast ballots the number of votes cast is:

(\( \frac{30}{100} \)) x 28,000 = \( \frac{840,000}{100} \) = 8,400

The mayor got 78% of the votes cast which is:

(\( \frac{78}{100} \)) x 8,400 = \( \frac{655,200}{100} \) = 6,552 votes.

To simplify a radical, factor out the perfect squares:

\( \sqrt{175} \)
\( \sqrt{25 \times 7} \)
\( \sqrt{5^2 \times 7} \)
5\( \sqrt{7} \)

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 + 50.7km + 13.4km
total distance = 64.2km

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.