NumberStudy Notes

Worked Example 2: Adding Surds

Part of Surds — GCSE Mathematics

This study notes covers Worked Example 2: Adding Surds within Surds for GCSE Mathematics. Revise Surds in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 8 of 14 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 8 of 14

Practice

14 questions

Recall

22 flashcards

Worked Example 2: Adding Surds

Simplify: √12 + √27

Solution

First simplify each surd:

√12 = √(4×3) = 2√3

√27 = √(9×3) = 3√3

Now add like surds:

2√3 + 3√3 = 5√3

Answer: 5√3

Keep building this topic

Read this section alongside the surrounding pages in Surds. That gives you the full topic sequence instead of a single isolated revision point.

Worked Example 1: Simplifying Worked Example 3: Multiplying Surds The Exact Truth What Are Surds?

Practice Questions for Surds

Which of these is the simplified form of √48?

A. 12√2
B. 4√3
C. 3√4
D. 6√2

1 markfoundation

Explain why it is preferable to write fractions in rationalized form rather than leaving a surd in the denominator.

2 markshigher

Quick Recall Flashcards

What are Like Surds?

Surds with the same root part Examples of like surds: • 3√2 and 5√2 (both have √2) • 2√7 and -4√7 (both have √7) Can add/subtract like surds: 3√2 + 5√2 = 8√2

What is a surd?

An irrational root that cannot be simplified to a whole number Examples: √2, √3, √5, ∛7 NOT surds: √4 = 2, √9 = 3 (these simplify to whole numbers)

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Worked Example 1: Simplifying

Worked Example 3: Multiplying Surds