Grade 11 Maths · Algebra

Check solutions of a surd equation

Check each answer by putting it back into the original equation with the square root, and reject any answer that does not work.

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4) Square root equations gr 11 | IntroKevinmathscience

Square Root Equations Grade 11 Maths Exam QuestionsMiss Martins Maths and Science

Square Root Equations Grade 11 Maths ExplainedMiss Martins Maths and Science

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Question 1.1.5 · May/June 2025 · Paper 1 · National (DBE) · 4 marks

1.1 Solve for

x

1.1.5

x + 3 x + 2 = 2

(4)

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

More past paper questions: check solutions of a surd equation

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3. Question 1.1.5 · May/June 2024 · Paper 1 · National (DBE) · 5 marks
1.1 Solve for x:
1.1.5 $\frac{x}{20 - x} = 1$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Isolate the surd $x = 20 - x$
  1 mark · Solve a linear equation
2. ✓
  Square both sides $x^{2} = 20 - x$
  1 mark · Solve a surd equation
3. ✓
  Standard form $x^{2} + x - 20 = 0$
  1 mark · Write a quadratic in standard form
4. ✓
  Solve quadratic factors $x = 4$ or $x = - 5$
  1 mark · Solve a quadratic by factorising
5. ✓
  Select valid solution after check $x = 4$
  1 mark · Check solutions of a surd equation
4. Question 1.3.1 · June 2024 · Paper 1 · Provincial · 5 marks
1.3 Solve for $x$ :
1.3.1 $x - 4 = - x - 2$ (5)
Show the memo (4 ticks)Memo
1. ✓
  Square both sides $(x - 4)^{2} = (- x - 2)^{2}$
  $x^{2} - 8 x + 16 = x - 2$
  1 mark · Solve a surd equation
2. ✓
  Standard form $x^{2} - 9 x + 18 = 0$
  1 mark · Write a quadratic in standard form
3. ✓
  Factorise and solve $(x - 6) (x - 3) = 0$
  $x = 6$ or $x = 3$
  1 mark · Solve a quadratic by factorising
4. ✓
  Check validityCheck $x = 6$ : LHS $6 - 4 = 2$ ; RHS $- 4 = - 2$ (Invalid)
  Check $x = 3$ : LHS $3 - 4 = - 1$ ; RHS $- 1 = - 1$ (Valid)
  2 marks · Check solutions of a surd equation
5. Question 1.1.4(b) · November 2025 · Paper 1 · Provincial · 4 marks
1.1 Solve for $x$ :
1.1.4 Given: $f (x) = \frac{x + 14}{x + 2}$
1.1.4(b) Solve for $x$ , if $f (x) = 1$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Isolating the surd $\frac{x + 14}{x + 2} = 1$
  $x + 14 = x + 2$
  1 mark · Solve a linear equation
2. ✓
  Squaring both sides $x + 14 = x^{2} + 4 x + 4$
  1 mark · Solve a surd equation
3. ✓
  Factors $x^{2} + 3 x - 10 = 0$
  $(x + 5) (x - 2) = 0$
  1 mark · Factorise a trinomial
4. ✓
  Answer with choice ( $- 5$ excluded) $x \neq = - 5$ or $x = 2$
  1 mark · Check solutions of a surd equation
6. Question 1.1.3 · March 2020 · Provincial · 5 marks
1.1 Solve for $x$ :
1.1.3 $x - 8 - 2 x = 0$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Isolate the surd $x = 8 - 2 x$
  1 mark · Solve a linear equation
2. ✓
  Square both sides $x^{2} = 8 - 2 x$
  $x^{2} + 2 x - 8 = 0$
  1 mark · Solve a surd equation
3. ✓
  Factorise and solve $(x + 4) (x - 2) = 0$
  $x = - 4$ or $x = 2$
  1 mark · Solve a quadratic by factorising
4. ✓
  Check validityCheck: If $x = - 4$ , $- 4 \neq = 8 - 2 (- 4)$
  Reject $x = - 4$
  1 mark · Check solutions of a surd equation
5. ✓
  Final solution $x = 2$ only
  1 mark · Check solutions of a surd equation

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