Irrational Numbers and Square Roots Flashcards

Grade 8 · Math · Flashcards

Review rational vs irrational numbers, perfect squares, and roots.

Flashcards

Rational number: Can be written as a fraction p/q. Terminating or repeating decimals are rational.
Irrational number: Cannot be written as fraction. Decimal never terminates or repeats. Examples: pi, sqrt(2).
Real numbers: All rational AND irrational numbers — every point on the number line.
Square root: sqrt(n) = number that when squared gives n. sqrt(25) = 5 because 5^2 = 25.
Perfect square: Whole number with a whole-number square root: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
Cube root: cbrt(n) = number that when cubed gives n. cbrt(8) = 2 because 2^3 = 8.
Estimating irrational roots: Find nearest perfect squares on either side: sqrt(50) is between 7 and 8 (since 7^2=49, 8^2=64).
sqrt(2): Approximately 1.414 — a classic irrational number.
sqrt(3): Approximately 1.732 — irrational.
Terminating decimal: Decimal that ends: 0.25, 0.5, 1.75. Always rational.
Repeating decimal: Decimal with a repeating block: 0.333..., 0.142857... Always rational.
Non-perfect square: sqrt(n) where n is not a perfect square is always irrational. Example: sqrt(5), sqrt(10).