To add or subtract radicals, the degree and radicand must be the same. For example, \(2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}\) but \(2\sqrt{2} + 2\sqrt{3}\) cannot be added because they have different radicands.

To multiply or divide radicals, multiply or divide the coefficients and radicands separately: \(x\sqrt{a} \times y\sqrt{b} = xy\sqrt{ab}\) and \({x\sqrt{a} \over y\sqrt{b}} = {x \over y}\sqrt{a \over b}\)

A rate is a ratio that compares two related quantities. Common rates are speed = \({distance \over time}\), flow = \({amount \over time}\), and defect = \({errors \over units}\).

Scientific notation is a method of writing very small or very large numbers. The first part will be a number between one and ten (typically a decimal) and the second part will be a power of 10. For example, 98,760 in scientific notation is 9.876 x 10⁴ with the 4 indicating the number of places the decimal point was moved to the left. A power of 10 with a negative exponent indicates that the decimal point was moved to the right. For example, 0.0123 in scientific notation is 1.23 x 10^-2.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately. For example, \(\sqrt{9 \over 16}\) = \({\sqrt{9}} \over {\sqrt{16}}\) = \({3 \over 4}\)