Grade 11 Maths · Algebra

Simplify and combine surds

Simplify square roots by taking out perfect squares, and add, subtract, multiply or divide them (for example √12 + √3 = 2√3 + √3 = 3√3).

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Grade 11 Maths Surds Introduction: Write a surd in simplest form without a calculatorMiss Martins Maths and Science

Grade 11 Maths Surd Rules: Addition and SubtractionMiss Martins Maths and Science

GCSE Maths - What on Earth are Surds??? And How do You Simplify Them? (Part 1/3) (2026/27 exams)Cognito

2) Simplify surds grade 11Kevinmathscience

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Question 1.2 · March 2025 · Provincial · 2 marks

1.2 Simplify without using a calculator:

384 + 24

(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: simplify and combine surds

Work each one out first, then open the memo and check every tick.

3. Question 8.2.1 · May/June 2024 · Paper 1 · National (DBE) · 3 marks
8.2 Determine:
8.2.1 $\frac{d}{d x} (4 x^{6} + 2 x^{2})$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Simplify first term to power form $2 x^{3}$
  1 mark · Simplify and combine surds
2. ✓
  Derive first term $6 x^{2}$
  1 mark · Differentiate using the power rule
3. ✓
  Derive second term $22 x$
  1 mark · Differentiate using the power rule
4. Question 2.2.2 · March 2019 · Provincial · 3 marks
2.2 Simplify without the use of a calculator:
2.2.2 $12 - 147 + 3^{1, 5}$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Simplify surds $23 - 73 + 33$
  2 marks · Simplify and combine surds
2. ✓
  Calculate sum $- 23$
  1 mark · Simplify and combine surds
5. Question 2.1 · March 2020 · Provincial · 3 marks
2.1 Simplify WITHOUT the use of a calculator:
$18 + 22 + \frac{1}{2}$
Write your answer with a rational denominator.(3)
Show the memo (3 ticks)Memo
1. ✓
  Simplify surds $18 = 32$
  Expression becomes: $32 + 22 + \frac{1}{2}$
  1 mark · Simplify and combine surds
2. ✓
  Rationalise denominator $52 + \frac{1}{2} \times \frac{2}{2}$
  $= 52 + \frac{2}{2}$
  1 mark · Rationalise a denominator
3. ✓
  Final answer $\frac{10 2 + 2}{2} = \frac{11 2}{2}$
  1 mark · Simplify and combine surds
6. Question 1.1 · June 2024 · Paper 2 · Provincial · 2 marks
In the diagram below, $A (- 2; 2)$ , $B (- 4; - 6)$ , $C (4; - 2)$ and $E (6; y)$ are the vertices of a quadrilateral with $A E ∣∣ BC$ . $D$ lies on $BC$ such that $A D ⊥ BC$ and $A C$ is drawn. $M (x; 2)$ is a point on line $EC$ .
1.1 Calculate the length of $BC$ . (Leave your answer in surd form.)(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute coordinates into distance formula $BC = (4 - (- 4))^{2} + (- 2 - (- 6))^{2}$
  1 mark · Calculate distance between two points
2. ✓
  Calculate final answer $BC = 80 = 45$
  1 mark · Simplify and combine surds

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