The equation for this sequence is:

a_n = a_n-1 + 8

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 + 8
a₆ = 33 + 8
a₆ = 41

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

9\( \sqrt{8} \) - 9\( \sqrt{2} \)
9\( \sqrt{4 \times 2} \) - 9\( \sqrt{2} \)
9\( \sqrt{2^2 \times 2} \) - 9\( \sqrt{2} \)
(9)(2)\( \sqrt{2} \) - 9\( \sqrt{2} \)
18\( \sqrt{2} \) - 9\( \sqrt{2} \)

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

If the tiger has consumed 144 pounds of food in 12 days that's \( \frac{144}{12} \) = 12 pounds of food per day. The tiger needs to consume 180 - 144 = 36 more pounds of food to reach 180 pounds total. At 12 pounds of food per day that's \( \frac{36}{12} \) = 3 more days.

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

6\( \sqrt{125} \) + 3\( \sqrt{5} \)
6\( \sqrt{25 \times 5} \) + 3\( \sqrt{5} \)
6\( \sqrt{5^2 \times 5} \) + 3\( \sqrt{5} \)
(6)(5)\( \sqrt{5} \) + 3\( \sqrt{5} \)
30\( \sqrt{5} \) + 3\( \sqrt{5} \)

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

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).