To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{44} \) = \( \frac{\frac{36}{4}}{\frac{44}{4}} \) = \( \frac{9}{11} \)

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.

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

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

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

1

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 45mph \times 8h \)
360 miles