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

3\( \sqrt{63} \) + 8\( \sqrt{7} \)
3\( \sqrt{9 \times 7} \) + 8\( \sqrt{7} \)
3\( \sqrt{3^2 \times 7} \) + 8\( \sqrt{7} \)
(3)(3)\( \sqrt{7} \) + 8\( \sqrt{7} \)
9\( \sqrt{7} \) + 8\( \sqrt{7} \)

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

The factors of a number are all positive integers that divide evenly into the number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{7} \) ÷ \( \frac{3}{8} \) = \( \frac{2}{7} \) x \( \frac{8}{3} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{7} \) x \( \frac{8}{3} \) = \( \frac{2 x 8}{7 x 3} \) = \( \frac{16}{21} \) = \(\frac{16}{21}\)

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).

The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 have in common.