PAss Functional Skills

Surds and roots

Surds and roots for GCSE Geography AQA Foundation: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Geography
  • Foundation
  • Spec R12 · R6 · R13
  • 9 min read
  • 9 revision boxes

Introduction

2 boxes
1 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.
Check the answer against an estimate before you move on, so a place-value slip is caught here.
4 rows

The surds and roots reference table

Work through the method one line at a time and write down what changes at each step.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
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
a2+b2=c2a^2 + b^2 = c^2
Row 2 column 4
Row 2 column 5
Row 3 column 1
Row 3 column 2
≈160\approx 160
Row 3 column 4
Row 3 column 5

Learning

5 boxes
4 steps

How to work with surds and roots

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

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

  • 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.
    a2+b2=c2a^2 + b^2 = c^2
5 steps

How to work with surds and roots

Check the answer against an estimate before you move on, so a place-value slip is caught here.
  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: 49=7\sqrt{49} = 7.
Answer: 49=7\sqrt{49} = 7
2 rules

Key facts: Surds and roots

Work through the method one line at a time and write down what changes at each step.
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.
    ≈160\approx 160

  • Rule 2

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

How to work with surds and roots

The specification wording is precise here, and the mark scheme follows that wording exactly.
  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: a2+b2=c2a^2 + b^2 = c^2.
Answer: ≈160\approx 160

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Examples

2 boxes
4 marks · worked

Worked example: 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.
1 marks · worked

Practice question 9: 49=7\sqrt{49} = 7

Practise the routine version until it is automatic, then move to the multi-step questions.

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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 Geography AQA Foundation paper?
Yes — it sits in the Sequences and graphs strand.