A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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

4\( \sqrt{6} \) x 8\( \sqrt{6} \)
(4 x 8)\( \sqrt{6 \times 6} \)
32\( \sqrt{36} \)

Now we need to simplify the radical:

32\( \sqrt{36} \)
32\( \sqrt{6^2} \)
(32)(6)
192

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 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.3km + 30.3km + 9.8km
total distance = 40.4km

To simplify a radical, factor out the perfect squares:

\( \sqrt{63} \)
\( \sqrt{9 \times 7} \)
\( \sqrt{3^2 \times 7} \)
3\( \sqrt{7} \)

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.