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

\( \frac{56\sqrt{56}}{8\sqrt{8}} \)
\( \frac{56}{8} \) \( \sqrt{\frac{56}{8}} \)
7 \( \sqrt{7} \)

Monica scored 81% on the test meaning she earned 81% of the possible points on the test. There were 280 possible points on the test so she earned 280 x 0.81 = 228 points. Each question is worth 4 points so she got \( \frac{228}{4} \) = 57 questions right.

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

\( \frac{4}{8} \) x \( \frac{4}{5} \) = \( \frac{4 x 4}{8 x 5} \) = \( \frac{16}{40} \) = \(\frac{2}{5}\)

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

7\( \sqrt{3} \) x 6\( \sqrt{3} \)
(7 x 6)\( \sqrt{3 \times 3} \)
42\( \sqrt{9} \)

Now we need to simplify the radical:

42\( \sqrt{9} \)
42\( \sqrt{3^2} \)
(42)(3)
126

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

8\( \sqrt{12} \) - 5\( \sqrt{3} \)
8\( \sqrt{4 \times 3} \) - 5\( \sqrt{3} \)
8\( \sqrt{2^2 \times 3} \) - 5\( \sqrt{3} \)
(8)(2)\( \sqrt{3} \) - 5\( \sqrt{3} \)
16\( \sqrt{3} \) - 5\( \sqrt{3} \)

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