To simplify a radical, factor out the perfect squares:

\( \sqrt{63} \)
\( \sqrt{9 \times 7} \)
\( \sqrt{3^2 \times 7} \)
3\( \sqrt{7} \)

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

2\( \sqrt{50} \) - 7\( \sqrt{2} \)
2\( \sqrt{25 \times 2} \) - 7\( \sqrt{2} \)
2\( \sqrt{5^2 \times 2} \) - 7\( \sqrt{2} \)
(2)(5)\( \sqrt{2} \) - 7\( \sqrt{2} \)
10\( \sqrt{2} \) - 7\( \sqrt{2} \)

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

The equation for this sequence is:

a_n = a_n-1 + 4

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4
a₆ = 17 + 4
a₆ = 21

49% of the water consumption is industrial use and 32% is personal use so (49% - 32%) = 17% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{17}{100} \) x 10,000 gallons = 1,700 gallons.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{9} \) x \( \frac{4}{7} \) = \( \frac{3 x 4}{9 x 7} \) = \( \frac{12}{63} \) = \(\frac{4}{21}\)