42% of the water consumption is industrial use and 10% is personal use so (42% - 10%) = 32% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{32}{100} \) x 35,000 gallons = 11,200 gallons.

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

\( \frac{35\sqrt{20}}{7\sqrt{4}} \)
\( \frac{35}{7} \) \( \sqrt{\frac{20}{4}} \)
5 \( \sqrt{5} \)

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:

\( \sqrt{\frac{4}{25}} \)
\( \frac{\sqrt{4}}{\sqrt{25}} \)
\( \frac{\sqrt{2^2}}{\sqrt{5^2}} \)
\(\frac{2}{5}\)

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:

\( \frac{6!}{3!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{6 \times 5 \times 4}{1} \)
\( 6 \times 5 \times 4 \)
120

To simplify a radical, factor out the perfect squares:

\( \sqrt{45} \)
\( \sqrt{9 \times 5} \)
\( \sqrt{3^2 \times 5} \)
3\( \sqrt{5} \)