PAss Functional Skills

Surds and roots

Surds and roots for A Level Combined Science AQA Foundation: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Combined Science
  • Foundation
  • Spec P13 · P2 · P18
  • 11 min read
  • 6 revision boxes

Introduction

2 boxes
4 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.
The examiner marks the working, so a correct answer with no method still drops marks.
4 rows

The surds and roots reference table

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: 49=7\sqrt{49} = 7.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
×10\times 10 moves every digit one column left
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

Learning

2 boxes
4 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: 34×25\frac{3}{4} \times \frac{2}{5}.
  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
2 rules

Key facts: Surds and roots

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.

  • 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.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 3

    How surds and roots behaves in the 3rd 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

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.
2 marks · worked

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

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

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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 Combined Science AQA Foundation paper?
Yes — it sits in the Statistics strand.