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

3\( \sqrt{48} \) + 5\( \sqrt{3} \)
3\( \sqrt{16 \times 3} \) + 5\( \sqrt{3} \)
3\( \sqrt{4^2 \times 3} \) + 5\( \sqrt{3} \)
(3)(4)\( \sqrt{3} \) + 5\( \sqrt{3} \)
12\( \sqrt{3} \) + 5\( \sqrt{3} \)

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

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

6z⁷ + 3z⁷
(6 + 3)z⁷
9z⁷

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-5z⁵ x 6z³
(-5 x 6)z^{(5 + 3)}
-30z⁸