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

8\( \sqrt{12} \) - 2\( \sqrt{3} \)
8\( \sqrt{4 \times 3} \) - 2\( \sqrt{3} \)
8\( \sqrt{2^2 \times 3} \) - 2\( \sqrt{3} \)
(8)(2)\( \sqrt{3} \) - 2\( \sqrt{3} \)
16\( \sqrt{3} \) - 2\( \sqrt{3} \)

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

A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

30,000 fans x \( \frac{5}{6} \) = \( \frac{150000}{6} \) = 25,000 fans.

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

36% of the water consumption is industrial use and 18% is personal use so (36% - 18%) = 18% more water is used for industrial purposes. 45,000 gallons are consumed daily so industry consumes \( \frac{18}{100} \) x 45,000 gallons = 8,100 gallons.

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).