The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,300
i = 0.08 x $1,300
i = $104

The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36]. They share 3 factors [1, 2, 4] making 4 the greatest factor 32 and 36 have in common.

To subtract these fractions, first find the lowest common multiple of their denominators. 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 share.

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

\( \frac{9 x 5}{9 x 5} \) - \( \frac{6 x 3}{15 x 3} \)

\( \frac{45}{45} \) - \( \frac{18}{45} \)

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

\( \frac{45 - 18}{45} \) = \( \frac{27}{45} \) = \(\frac{3}{5}\)

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

\( \frac{21\sqrt{35}}{7\sqrt{7}} \)
\( \frac{21}{7} \) \( \sqrt{\frac{35}{7}} \)
3 \( \sqrt{5} \)

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{52} \) = \( \frac{\frac{36}{4}}{\frac{52}{4}} \) = \( \frac{9}{13} \)