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

5\( \sqrt{2} \) x 3\( \sqrt{3} \)
(5 x 3)\( \sqrt{2 \times 3} \)
15\( \sqrt{6} \)

To subtract 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 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

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

\( \frac{4 x 5}{3 x 5} \) - \( \frac{4 x 3}{5 x 3} \)

\( \frac{20}{15} \) - \( \frac{12}{15} \)

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

\( \frac{20 - 12}{15} \) = \( \frac{8}{15} \) = \(\frac{8}{15}\)

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

1

The equation for this sequence is:

a_n = a_n-1 + 1

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 1
a₆ = 5 + 1
a₆ = 6