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

\( \frac{9\sqrt{14}}{3\sqrt{7}} \)
\( \frac{9}{3} \) \( \sqrt{\frac{14}{7}} \)
3 \( \sqrt{2} \)

If 75% of the town's 10,000 voters cast ballots the number of votes cast is:

(\( \frac{75}{100} \)) x 10,000 = \( \frac{750,000}{100} \) = 7,500

The mayor got 84% of the votes cast which is:

(\( \frac{84}{100} \)) x 7,500 = \( \frac{630,000}{100} \) = 6,300 votes.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{8 x 3}{3 x 3} \) + \( \frac{9 x 1}{9 x 1} \)

\( \frac{24}{9} \) + \( \frac{9}{9} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{24 + 9}{9} \) = \( \frac{33}{9} \) = 3\(\frac{2}{3}\)

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:

\( \sqrt{\frac{16}{36}} \)
\( \frac{\sqrt{16}}{\sqrt{36}} \)
\( \frac{\sqrt{4^2}}{\sqrt{6^2}} \)
\(\frac{2}{3}\)

By buying two shirts, Frank will save $30 x \( \frac{30}{100} \) = \( \frac{$30 x 30}{100} \) = \( \frac{$900}{100} \) = $9.00 on the second shirt.

So, his total cost will be
$30.00 + ($30.00 - $9.00)
$30.00 + $21.00
$51.00