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

\( \frac{2}{6} \) x \( \frac{3}{8} \) = \( \frac{2 x 3}{6 x 8} \) = \( \frac{6}{48} \) = \(\frac{1}{8}\)

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

5\( \sqrt{20} \) - 6\( \sqrt{5} \)
5\( \sqrt{4 \times 5} \) - 6\( \sqrt{5} \)
5\( \sqrt{2^2 \times 5} \) - 6\( \sqrt{5} \)
(5)(2)\( \sqrt{5} \) - 6\( \sqrt{5} \)
10\( \sqrt{5} \) - 6\( \sqrt{5} \)

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

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

\( \frac{45\sqrt{36}}{9\sqrt{9}} \)
\( \frac{45}{9} \) \( \sqrt{\frac{36}{9}} \)
5 \( \sqrt{4} \)

The factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 the greatest factor 60 and 80 have in common.

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

9\( \sqrt{27} \) + 3\( \sqrt{3} \)
9\( \sqrt{9 \times 3} \) + 3\( \sqrt{3} \)
9\( \sqrt{3^2 \times 3} \) + 3\( \sqrt{3} \)
(9)(3)\( \sqrt{3} \) + 3\( \sqrt{3} \)
27\( \sqrt{3} \) + 3\( \sqrt{3} \)

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