Simplifying Surds Flashcards

An irrational number that cannot be simplified to remove a square root (or cube root, etc.).

Expressing a surd in its simplest form by factoring out square numbers.

5√2 (since √50 = √(25 × 2) = √25 × √2 = 5√2).

6√2 (since √72 = √(36 × 2) = √36 × √2 = 6√2).

Multiply the numbers inside the square roots, e.g., √2 × √3 = √6.

Divide the numbers inside the square roots, e.g., √8 ÷ √2 = √(8 ÷ 2) = √4 = 2.

You can only add or subtract like surds, e.g., 3√2 + 2√2 = 5√2.

Removing a surd from the denominator by multiplying numerator and denominator by the surd.

Multiply numerator and denominator by √3: (1/√3) × (√3/√3) = √3/3.

Multiply numerator and denominator by √2: (5/(2√2)) × (√2/√2) = 5√2/4.