Understanding Surds and Indices in WJEC AS Pure Mathematics

Surds and Indices: Essential Rules

Ever wondered what to do when you can't simplify a square root? That's where surds come in - they're simply the square root of numbers that aren't perfect squares, like √2 or expressions containing them such as 5+√3.

Surds follow two key rules that make calculations much easier. First, √ab = √a × √b, which means you can split square roots across multiplication. Second, √(a/b) = √a/√b, letting you separate square roots in fractions.

Indices (or powers) have their own set of rules that become second nature with practice. When multiplying powers with the same base, you add the indices: M^a × M^b = M^$a+b$. When dividing, you subtract them: M^a ÷ M^b = M^$a-b$.

Quick Tip: Remember that any number to the power of 0 equals 1, and negative powers create fractions: M^$-a$ = 1/M^a.

The power of a power rule is particularly useful: $M^a$^b = M^(a×b). You'll also encounter fractional powers, where (√M)^b = M^$b/2$, connecting surds and indices together.