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

4\( \sqrt{8} \) x 5\( \sqrt{5} \)
(4 x 5)\( \sqrt{8 \times 5} \)
20\( \sqrt{40} \)

Now we need to simplify the radical:

20\( \sqrt{40} \)
20\( \sqrt{10 \times 4} \)
20\( \sqrt{10 \times 2^2} \)
(20)(2)\( \sqrt{10} \)
40\( \sqrt{10} \)

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

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

5\( \sqrt{27} \) + 7\( \sqrt{3} \)
5\( \sqrt{9 \times 3} \) + 7\( \sqrt{3} \)
5\( \sqrt{3^2 \times 3} \) + 7\( \sqrt{3} \)
(5)(3)\( \sqrt{3} \) + 7\( \sqrt{3} \)
15\( \sqrt{3} \) + 7\( \sqrt{3} \)

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

The equation for this sequence is:

a_n = a_n-1 + 2(n - 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 + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.