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:

\( \sqrt{\frac{4}{4}} \)
\( \frac{\sqrt{4}}{\sqrt{4}} \)
\( \frac{\sqrt{2^2}}{\sqrt{2^2}} \)
1

The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 have in common.

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

\( \frac{15\sqrt{10}}{3\sqrt{2}} \)
\( \frac{15}{3} \) \( \sqrt{\frac{10}{2}} \)
5 \( \sqrt{5} \)

49% of the water consumption is industrial use and 27% is personal use so (49% - 27%) = 22% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{22}{100} \) x 10,000 gallons = 2,200 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 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{44} \) = \( \frac{\frac{20}{4}}{\frac{44}{4}} \) = \( \frac{5}{11} \)