Sections 8.3 and 8.4 Simplifying Radicals Adding and Subtracting Radicals

Two Important Rules

Examples

Three Very Important Lists Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100,…,x 2, x 4, x 6, x 8,… Perfect Cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000,…, x 3, x 6, x 9, x 12,… Perfect Fourths: 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000,…, x 4, x 8, x 12, x 16,…

Simplifying Radicals: Coefficients Method One: find the largest perfect factor of that number. Method Two: use prime factorization and circle groups according to the index.

Simplifying Radicals: Variables Divide the exponent by the index. The quotient comes out, the remainder stays in.

Examples

Application of Simplifying Radicals: The Distance Formula Given two points (x 1, y 1 ) and (x 2, y 2 ), the distance d between the two points is given by: Examples: find the distance between (8, 13) and (2, 5) (-1, 2) and (5, 3)

Like Radical Terms Same index Same radicand The number outside the radical is called a coefficient.

Adding and Subtracting Radicals Only like radical terms can be added or subtracted. Add or subtract the coefficients. Do NOT add or subtract the radicands. Make sure your radicals are completely simplified. Some unlike radicals become like radicals and can then be added or subtracted.

Examples