Curriculum
Course: Mathematics — Second Preparatory
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Curriculum

Mathematics — Second Preparatory

Unit 1: Real Numbers

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Unit 2: Algebra

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Unit 3: Geometry

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Unit 4: Statistics

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Text lesson

Square and Cube Root Laws

Mathematics — Second Preparatory

Square and Cube Root Laws

The root laws

The root laws

  • Let a and b be positive numbers. Then:
Law Example
√(a × b) = √a × √b √(4 × 9) = 2 × 3 = 6
√(a ÷ b) = √a ÷ √b √(36 ÷ 9) = 6 ÷ 3 = 2
3√(a × b) = 3√a × 3√b 3√(8 × 27) = 2 × 3 = 6
√(a²) = a for positive a √(7²) = 7
  • To simplify a square root, we take out the largest perfect square that divides the number under it.
  • For example, √72 = √36 × √2 = 6√2.
  • The same law applies to cube roots 3√54 = 3√(27 × 2) = 3 3√2, because 3√27 = 3. Check: (3 3√2)3 = 27 × 2 = 54.
  • Note for cube roots we do not need the absolute value, because 3√(a³) = a for every real number a, whether positive or negative.
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