Radical Expressions and Equations Flashcards

Grade 10 · Math · Flashcards

Essential vocabulary and rules for working with radicals and radical equations.

Flashcards

Radical expression: An expression that includes a root symbol (√, ∛, etc.)
Radicand: The number or expression underneath the radical sign
Index of a radical: The small number indicating which root; 2 (square root) is default, 3 = cube root
Simplest radical form: No perfect square (or nth-power) factors in radicand; no radical in denominator
Product rule for radicals: √a · √b = √(ab) for a,b ≥ 0
Quotient rule for radicals: √a / √b = √(a/b) for a ≥ 0, b > 0
Rationalizing the denominator: Eliminating a radical from the denominator by multiplying numerator and denominator by that radical
Like radicals: Radicals with the same index and the same radicand; can be added/subtracted
Extraneous solution: An answer that emerges from solving algebraically but fails when substituted into the original equation
Rational exponent x^(1/n): Equal to ⁿ√x (the nth root of x)
Rational exponent x^(m/n): Equal to (ⁿ√x)^m — take the nth root, then raise to the mth power
Solving a radical equation: Isolate the radical, raise both sides to the power of the index, solve, then CHECK for extraneous solutions
Can you take the square root of a negative number (in reals)?: No — √(negative) is not a real number; it's imaginary