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

7\( \sqrt{63} \) + 4\( \sqrt{7} \)
7\( \sqrt{9 \times 7} \) + 4\( \sqrt{7} \)
7\( \sqrt{3^2 \times 7} \) + 4\( \sqrt{7} \)
(7)(3)\( \sqrt{7} \) + 4\( \sqrt{7} \)
21\( \sqrt{7} \) + 4\( \sqrt{7} \)

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

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

You have 12 out of the total of 400 raffle tickets sold so you have a (\( \frac{12}{400} \)) x 100 = \( \frac{12 \times 100}{400} \) = \( \frac{1200}{400} \) = 3% chance to win the raffle.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).