Surd

Definition

A surd is a root that can't be simplified to a rational number, such as √2, √5 or ∛4. Surds are left in simplest form (√48 = 4√3) instead of being rounded, and denominators are rationalised.

Worked example

√48 − 2√12 = 4√3 − 4√3 = 0.

Rationalise 6/√3: multiply by √3/√3 to get 6√3/3 = 2√3.

Solve √(x + 7) = x − 5: squaring gives x = 9 or x = 2, but only x = 9 checks out.

Where it appears in the exam

Surd is part of the algebra section of CAPS Grade 11 Mathematics and is examined in Paper 1 of the November exam.

Step-by-step method

1. Write the number under the root as a perfect square times another factor.
2. Take the square root of the perfect square out of the root.
3. Add or subtract only like surds.
4. In surd equations, check every answer in the original equation.

Common mistake

Writing √(a + b) = √a + √b, which is false.

Related algebra terms

• Discriminant
• Difference of two squares
• Exponential equation
• Quadratic inequality

Frequently asked questions

What does surd mean in Grade 11 Maths?

A surd is a root that can't be simplified to a rational number, such as √2, √5 or ∛4. Surds are left in simplest form (√48 = 4√3) instead of being rounded, and denominators are rationalised.

Which paper tests surd in Grade 11?

Surd belongs to the Algebra section of CAPS Grade 11 Mathematics, which is examined in Paper 1 of the November exam.

How do I practise questions involving surd?

Snap a question that uses surd into Snap&Learn with your grade set to Grade 11, or work through the Grade 11 topic guide and practice papers.