If any of the radicand's factors are square numbers then the surd can be simplified.
Algebraic factors that are square values also mean the surd can be simplified.
Common misconception
Pupils may not multiply the existing coefficient with the coefficient of the simplified surd.
Replace the unsimplified surd with the simplified form within the original expression so pupils can see they need to multiply coefficients.
Keywords
Product of primes - Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.
Simplest form - A surd is in its simplest form when the radicand is an integer with no perfect square factors greater than 1.
Pupils may grasp this quickly and want to rush ahead. A firm understanding of the basics are needed here though as otherwise pupils may struggle as their surd manipulation skills increase.
