Working with Surds - The Basics
Think of surds like algebra terms - you can only add or subtract surds when they have the same number under the square root sign. For example, 5√2 + 3√2 = 8√2, but you can't simplify 4√2 + 3√3 because the numbers inside are different.
Simplifying surds is all about spotting square number factors. Keep a list handy: 1, 4, 9, 16, 25, 36, 49... When you see √12, notice that 12 = 4 × 3, so √12 = √4 × √3 = 2√3.
Multiplying surds becomes straightforward once you remember that √5 × √5 = 5 (the square root disappears). For different surds like √8 × √10, multiply to get √80, then simplify: √80 = √(16 × 5) = 4√5.
Quick tip: When expanding brackets like 3 + √2$$2 + √5, use FOIL just like with normal algebra - multiply each term in the first bracket by each term in the second.
