Module 3 · Advanced Algebra
Chapter 15: Radical Expressions
Advanced Math
4 topics
What this chapter covers
The 4 topics below make up Radical Expressions on the Digital SAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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Formula Reference Sheet
This chapter
Working with radicals
| Product rule | √(ab) = √a · √b |
|---|---|
| Quotient rule | √(a/b) = √a / √b |
| Simplify | pull out perfect-square factors |
| Like radicals | add/subtract only matching roots |
Conversions & equations
| Rational exponent | √x = x^(1/2), ∛x = x^(1/3) |
|---|---|
| Rationalize | multiply by √b/√b (or the conjugate) |
| Solve √x = k | square both sides; check answers |
Digital SAT reference
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |
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