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Surds and roots

Surds and roots for GCSE Combined Science OCR Foundation: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • OCR
  • Combined Science
  • Foundation
  • Spec S17 · S19 · S10
  • 9 min read
  • 8 revision boxes

Introduction

2 boxes
2 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.
Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ×10\times 10 moves every digit one column left.
4 rows

The surds and roots reference table

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: ≈160\approx 160.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
49=7\sqrt{49} = 7
Row 1 column 4
Row 2 column 1
Row 2 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 4

Learning

4 boxes
4 steps

How to work with surds and roots

This idea appears again in the higher-mark questions, so it is worth over-learning.
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: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: ×10\times 10 moves every digit one column left
2 rules

Key facts: Surds and roots

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: ≈160\approx 160.

  • 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.
    x2+5x+6=0x^2 + 5x + 6 = 0
3 steps

How to work with surds and roots

Practise the routine version until it is automatic, then move to the multi-step questions.
  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.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ≈160\approx 160.
Answer: ≈160\approx 160
3 rules

Key facts: 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: a2+b2=c2a^2 + b^2 = c^2.

  • Rule 1

    How surds and roots behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How surds and roots behaves in the 2nd of the cases the specification names.
    ≈160\approx 160

  • Rule 3

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

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Examples

2 boxes
3 marks · worked

Worked example: surds and roots

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

Practice question 8: 49=7\sqrt{49} = 7

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

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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 Combined Science OCR Foundation paper?
Yes — it sits in the Sequences and graphs strand.