A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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).

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{36}{49}} \)
\( \frac{\sqrt{36}}{\sqrt{49}} \)
\( \frac{\sqrt{6^2}}{\sqrt{7^2}} \)
\(\frac{6}{7}\)

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

5\( \sqrt{75} \) + 5\( \sqrt{3} \)
5\( \sqrt{25 \times 3} \) + 5\( \sqrt{3} \)
5\( \sqrt{5^2 \times 3} \) + 5\( \sqrt{3} \)
(5)(5)\( \sqrt{3} \) + 5\( \sqrt{3} \)
25\( \sqrt{3} \) + 5\( \sqrt{3} \)

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