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

3\( \sqrt{12} \) - 5\( \sqrt{3} \)
3\( \sqrt{4 \times 3} \) - 5\( \sqrt{3} \)
3\( \sqrt{2^2 \times 3} \) - 5\( \sqrt{3} \)
(3)(2)\( \sqrt{3} \) - 5\( \sqrt{3} \)
6\( \sqrt{3} \) - 5\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them:

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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).

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

46,000 fans x \( \frac{2}{3} \) = \( \frac{92000}{3} \) = 30,667 fans.

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