1. Radicals Review

2. 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

3. Simplifying Radicals Perfect Squares: Non-Perfect Squares: 49 𝑥 2 𝑦 620 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 𝑧 2
4 5

4. It’s just like combining like terms, but with “like radicals” instead
−3 2𝑥 𝑥
Add/Sub Radicals

5. 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

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