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Surds and roots

Surds and roots for GCSE Environmental Science Edexcel: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • Edexcel
  • Environmental Science
  • Spec G19
  • 7 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.
Work through the method one line at a time and write down what changes at each step.
Worth knowing: ×10\times 10 moves every digit one column left.
6 rows

The surds and roots reference table

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
49=7\sqrt{49} = 7
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 2 column 4
Row 2 column 5

Learning

4 boxes
4 steps

How to work with surds and roots

Read the units in the question before you start; a converted unit is the most common slip.
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: ×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: a2+b2=c2a^2 + b^2 = c^2.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Surds and roots

The specification wording is precise here, and the mark scheme follows that wording exactly.

  • Rule 1

    How surds and roots behaves in the 1st of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 2

    How surds and roots behaves in the 2nd of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 3

    How surds and roots behaves in the 3rd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2
4 steps

How to work with surds and roots

Work through the method one line at a time and write down what changes at each step.
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: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: 49=7\sqrt{49} = 7
2 rules

Key facts: Surds and roots

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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.
    ≈160\approx 160

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Examples

2 boxes
2 marks · worked

Worked example: surds and roots

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
3 marks · worked

Practice question 8: a2+b2=c2a^2 + b^2 = c^2

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.

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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 Environmental Science Edexcel paper?
Yes — it sits in the Statistics strand.