Dealing With Surds (Leaving Cert Mathematics): Flashcards

Numbers written as $\frac{a}{b}$, $a$, $b$ integers, $b \neq 0$

Numbers that cannot be written as exact fractions

Square roots with no exact whole number value

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

$\frac{\sqrt{a}}{\sqrt{b}}$

Largest perfect square factor taken out

Only when same irrational parts (like terms)

Multiply rational & irrational parts separately

Isolate the square root on one side

Square both sides to eliminate square root

Check solutions in original equation

Squaring can introduce false solutions

Positive value only: $5$ not $\pm 5$