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Surds and roots

Surds and roots for GCSE French Edexcel: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • Edexcel
  • French
  • Spec N16 · N6
  • 8 min read
  • 8 revision boxes

Introduction

2 boxes
3 min read

What is surds and roots?

Listen to this box

Transcript

A short spoken summary of surds and roots and where it is used.

A spoken walk-through of surds and roots before you read the notes.
Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing surds and roots laid out step by step

The same idea drawn out, so the method is visible.
2 rows

The surds and roots reference table

Practise the routine version until it is automatic, then move to the multi-step questions.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
×10\times 10 moves every digit one column left
Row 1 column 4
Row 2 column 1
Row 2 column 2
≈160\approx 160
Row 2 column 4
Row 3 column 1
Row 3 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 3 column 4
Row 4 column 1
Row 4 column 2
×10\times 10 moves every digit one column left
Row 4 column 4

Learning

4 boxes
4 steps

How to work with surds and roots

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: ×10\times 10 moves every digit one column left.
  1. Read the question and write down what is being asked for.
  2. Set out the working for surds and roots in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Surds and roots

This idea appears again in the higher-mark questions, so it is worth over-learning.

  • Rule 1

    How surds and roots behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How surds and roots behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How surds and roots behaves in the 3rd of the cases the specification names.
    49=7\sqrt{49} = 7
3 steps

How to work with surds and roots

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing surds and roots laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 49=7\sqrt{49} = 7.
  1. Read the question and write down what is being asked for.
  2. Set out the working for surds and roots in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ≈160\approx 160.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
2 rules

Key facts: Surds and roots

Practise the routine version until it is automatic, then move to the multi-step questions.
The layout below is the one the mark scheme expects.

Diagram showing surds and roots laid out step by step

The same idea drawn out, so the method is visible.

  • Rule 1

    How surds and roots behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

    How surds and roots behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 3

    How surds and roots behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

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Examples

2 boxes
2 marks · worked

Worked example: surds and roots

Check the answer against an estimate before you move on, so a place-value slip is caught here.
2 marks · worked

Practice question 8: ≈160\approx 160

The examiner marks the working, so a correct answer with no method still drops marks.

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Common questions

How many marks is surds and roots usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE French Edexcel paper?
Yes — it sits in the Sequences and graphs strand.