Radical Expressions Flashcards

Grade 9 · Math · Flashcards

Core rules, definitions, and solved examples for working fluently with radical expressions.

Flashcards

Product rule for radicals: √a · √b = √(ab), provided a ≥ 0 and b ≥ 0
Quotient rule for radicals: √(a/b) = √a / √b, provided a ≥ 0 and b > 0
Simplify √(a²): |a| (absolute value of a, since square roots are non-negative)
Rationalize 1/√n: Multiply by √n/√n to get √n/n
Conjugate of (a + √b): (a − √b); their product eliminates the radical: (a + √b)(a − √b) = a² − b
Add √12 + √27: 2√3 + 3√3 = 5√3 (simplify first, then combine like radicals)
Simplify √(16/25): 4/5 (take the square root of numerator and denominator separately)
Cube root of −27: −3, because (−3)³ = −27
Simplify 6√5 / (3√5): 2 (the √5 terms cancel, 6/3 = 2)
Multiply (2 + √3)²: 4 + 4√3 + 3 = 7 + 4√3
When can you combine radicals?: Only when they have the same index AND the same radicand (like radicals)
Simplify ∛(−8x³): −2x (cube root of a negative number is negative)
√(-4) in real numbers: Undefined — square roots of negative numbers are not real numbers
Simplify √(x² + 6x + 9): |x + 3| or (x + 3) for x ≥ −3, since x² + 6x + 9 = (x + 3)²