The factors of a number are all positive integers that divide evenly into the number. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

To multiply terms with radicals, multiply the coefficients and radicands separately:

2\( \sqrt{8} \) x 5\( \sqrt{2} \)
(2 x 5)\( \sqrt{8 \times 2} \)
10\( \sqrt{16} \)

Now we need to simplify the radical:

10\( \sqrt{16} \)
10\( \sqrt{4^2} \)
(10)(4)
40

42% of the water consumption is industrial use and 29% is personal use so (42% - 29%) = 13% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{13}{100} \) x 35,000 gallons = 4,550 gallons.

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{68} \) = \( \frac{\frac{20}{4}}{\frac{68}{4}} \) = \( \frac{5}{17} \)

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:

34,000 fans x \( \frac{2}{3} \) = \( \frac{68000}{3} \) = 22,667 fans.