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.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{5!} \)
\( \frac{3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4} \)
\( \frac{1}{20} \)

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

4\( \sqrt{12} \) + 5\( \sqrt{3} \)
4\( \sqrt{4 \times 3} \) + 5\( \sqrt{3} \)
4\( \sqrt{2^2 \times 3} \) + 5\( \sqrt{3} \)
(4)(2)\( \sqrt{3} \) + 5\( \sqrt{3} \)
8\( \sqrt{3} \) + 5\( \sqrt{3} \)

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

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

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:

\( \sqrt{\frac{64}{9}} \)
\( \frac{\sqrt{64}}{\sqrt{9}} \)
\( \frac{\sqrt{8^2}}{\sqrt{3^2}} \)
\( \frac{8}{3} \)
2\(\frac{2}{3}\)