Karteikarten: Understanding Surds and the Real Number System — 18 Karten

Real Number System — hierarchy?

N ⊂ Z ⊂ Q ⊂ R

Surds — definition?

Irrational roots expressed with radicals.

Simplify √45 — method?

Factor as √9×5, simplify to 3√5.

Surds — multiplication rule?

√a × √b = √(a×b).

Rationalising denominators — purpose?

Eliminate surds from the denominator.

Number classification — key test?

Decimal pattern or fraction form.

Order surds — comparison method?

Approximate decimal or compare radicands.

Square root — relation to powers?

a^(1/2), inverse of squaring.

Cube root — example?

3√−1728 = -12, since (-12)^3 = -1728.

Surd expression — forming?

Express radicand as perfect square/cube factors.

Adding surds — condition?

Same radical part (like terms).

Simplify √128 — step?

√64×2 = 8√2.

Order √6, √7 — which larger?

√7 > √6, compare decimal approximations.

Rationalising 1/√5 — result?

√5/5 after multiplying numerator and denominator by √5.

Classify 3π — rational or irrational?

Irrational, cannot be expressed as fraction.

Square root of 25 — rational?

Yes, equals 5.

Surd — in simplest form?

No perfect square or cube factors inside radical.

Express 8√2 as a surd?

8√2 is already a surd expression.