To simplify a radical, factor out the perfect squares:

\( \sqrt{12} \)
\( \sqrt{4 \times 3} \)
\( \sqrt{2^2 \times 3} \)
2\( \sqrt{3} \)

To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{56} \) = \( \frac{\frac{32}{8}}{\frac{56}{8}} \) = \( \frac{4}{7} \)

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 $900
i = 0.07 x $900

No payments were made so the total amount due is the original amount + the accumulated interest:

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:

\( \frac{2!}{4!} \)
\( \frac{2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4 \times 3} \)
\( \frac{1}{12} \)

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

6\( \sqrt{45} \) + 6\( \sqrt{5} \)
6\( \sqrt{9 \times 5} \) + 6\( \sqrt{5} \)
6\( \sqrt{3^2 \times 5} \) + 6\( \sqrt{5} \)
(6)(3)\( \sqrt{5} \) + 6\( \sqrt{5} \)
18\( \sqrt{5} \) + 6\( \sqrt{5} \)

Now that the radicands are identical, you can add them together: