SAT Math · Study & Practice

Radical Expressions

Radicals — square roots and beyond — appear across SAT Advanced Math, often alongside exponents. This chapter covers simplifying radicals, operations with radicals, rationalizing denominators and solving radical equations. Read each topic, try the problems with the hint ladder, then take the 8-question topic test.

Topics

1 Simplifying Radicals 4 worked · 5 practice · 8-Q test Start → 2 Operations with Radicals 4 worked · 5 practice · 8-Q test Start → 3 Rationalizing Denominators 4 worked · 5 practice · 8-Q test Start → 4 Radical Equations 4 worked · 5 practice · 8-Q test Start →

Chapter test

📝 Radical Expressions — Chapter Test

25 fresh questions · timed · full solutions

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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°