Understanding Surds and Basic Rules
Ever wondered why some square roots give you neat whole numbers whilst others don't? Rational numbers like √36 = 6 give exact values, but surds (or irrationals) like √2 ≈ 1.4 go on forever without a pattern.
The first rule of surds is your best mate: √a × √b = √ab. This works both ways, so √15 can become √3 × √5. When you multiply a surd by itself, you get the number inside - so √3 × √3 = 3.
To simplify surds like √12, split the number into factors where one is a perfect square. So √12 = √4 × √3 = 2√3. Always use the biggest square number you can find - it makes life easier.
The second rule handles division: √a/√b = √(a/b). This is dead useful when you're working with fractions containing surds.
Top Tip: When adding and subtracting surds, treat them like algebra variables. You can do 4√2 + 6√2 = 10√2, but you can't simplify √2 + √3!
