Concept preview

What you will be able to do

1. 01Simplify radicals by removing perfect-square factors, and convert entire ↔ mixed radicals
2. 02Add, subtract, and multiply radicals
3. 03Rationalise denominators, including with conjugates

You met square roots in Grade 9 with the Pythagorean theorem. The radical $\sqrt{a}$ asks a simple question: *what number, squared, gives $a$?* Since $5^2 = 25$, we have $\sqrt{25} = 5$. Numbers like $25, 36, 49$ are perfect squares — their roots are whole numbers. But most numbers, like $12$ or $2$, are not, and their roots are irrational decimals that go on forever. This lesson is about handling those messy roots exactly, without rounding.