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Year 9 · Place Value

Simplify surds

A surd is a square root that is not a whole number, like √12. Simplify by pulling out square factors.

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How to do it

  1. Find the biggest square number that divides in.
  2. Split: √12 = √4 × √3 = 2√3.
  3. Like surds add: 2√3 + 5√3 = 7√3.

Worked example

Simplify √63
63 = 9 × 7, and √9 = 3, so √63 = 3√7.
Answer: 3√7

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√a + √b is not √(a + b).

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