PAss Functional Skills

Surds and roots

Surds and roots for A Level Engineering AQA Higher: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Engineering
  • Higher
  • Spec N2
  • 6 min read
  • 6 revision boxes

Introduction

2 boxes
4 min read

What is surds and roots?

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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.
The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: 49=7\sqrt{49} = 7.
5 rows

The surds and roots reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 1
Row 2 column 2
×10\times 10 moves every digit one column left
Row 3 column 1
Row 3 column 2
49=7\sqrt{49} = 7
Row 4 column 1
Row 4 column 2
×10\times 10 moves every digit one column left

Learning

2 boxes
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: x2+5x+6=0x^2 + 5x + 6 = 0.
  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: 49=7\sqrt{49} = 7
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.
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.
    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.
    34×25\frac{3}{4} \times \frac{2}{5}

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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 6: 34×25\frac{3}{4} \times \frac{2}{5}

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

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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 A Level Engineering AQA Higher paper?
Yes — it sits in the Sequences and graphs strand.