Number · Surds
Chapter 1 · 4
The idea
Simplifying surds
Why surds are kept as exact values, why √(ab) = √a × √b lets you pull square factors out, and how to collect like surds — and why √a + √b is not √(a+b).
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Number · Surds
Simplifying surds
Why surds are kept as exact values, why √(ab) = √a × √b lets you pull square factors out, and how to collect like surds — and why √a + √b is not √(a+b).
Why it works
Exact, not approximate
A surd is a root that isn't a whole number — , , . We keep them as symbols instead of decimals because they are exact: squared is exactly , while — close, but wrong. When a question says "give an exact answer" or "in the form ", a rounded decimal scores nothing.The one rule everything comes from
Every surd manipulation on the paper flows from a single fact:Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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