Radicals Review

The radicand (the expression inside the radical) must be greater than or equal to 0. Trying to square root negative numbers does not have any real solutions. Examples: Find the domain of each radical function. 𝑓 𝑥 = 𝑥+5 𝑓 𝑥 =4 3𝑥−10 𝑓 𝑥 =− −4𝑥 Domain

Simplifying Radicals Perfect Squares: Non-Perfect Squares: 49 𝑥 2 𝑦 6 20 45 4 28 −4 75 Simplifying Radicals 𝑥 3 𝑦 7 𝑥 21 𝑥 9 𝑦 8 6 49 𝑥 3 𝑦 4 𝑧 2 5𝑥 𝑦 5 45 𝑧 2 4 5

It’s just like combining like terms, but with “like radicals” instead 2 7 +9 7 −3 2𝑥 +5 2 +8 2𝑥 2 80 +3 45 Add/Sub Radicals

Multiply together everything outside the radicals together Multiply together everything outside the radicals together. Multiply everything inside the radicals together. 2 6 ∙8 12 4 5𝑥 ∙3 8𝑥 7 3𝑥 𝑦 5 ∙2 3 𝑥 3 𝑦 Multiplying Radicals

Solve Radical Equations 𝑥 =9 𝑥 −6=2 𝑥−6 =3 2 5𝑥 =10 2𝑥+1 = 3𝑥+5 Solve Radical Equations