Manipulating surds (AQA GCSE Further Maths): Flashcards

Expression with √ that can't simplify to a whole number

Maintains exact values/precision without rounding errors

Numbers expressible as whole number squared (e.g. $4 = 2^2$)

$\sqrt{a} \times \sqrt{b}$

$2\sqrt{2}$

Only combine terms with same square root part

$a$

$a$

$a^2 - b$

Removing surds from denominator to make it rational

Multiply top and bottom by $\frac{\sqrt{a}}{\sqrt{a}}$

$(a + b)$

Multiply by conjugate (flip middle sign)