Surds

Tutorial Videos

Surds – Corbettmaths

Corbett Maths Surds

Online Platforms (with Videos & Exercises)

Activities & Resources

• Pixi Maths
  • Introduction to Surds ppt
• Andy Lutwyche
  • Spiders
  • Codebreakers
  • Clumsy Clive
  • Match Up
  • (Partially Simplified) Codebreakers
  • (Partially Simplified) Codebreaker
  • Partially Simplified
  • Hulk
• Math = Love (Sarah Carter)
  • Simplifying Square Roots Bingo
  • Perfect Squares list
  • Which is the Smallest? task
  • Simplifying Surds foldable
  • Simplifying Surds Workmat
  • Simplifying Surds Puzzle
  • Steps for Simplifying Surds
  • Parts of a Radical Organiser
  • Square Roots Dice Review
• Resourceaholic
  • Surds
• Spain Park HS
  • Simplifying Radicals Tarsia
• Don Steward
  • Pythagoras and Surd Forms✦
  • Irrationality of the Square Root of 2
  • Unusual Square Roots
  • Surd Simplification✦
• Ben Sparks (GeoGebra)
  • Surd Spiral (Spiral of Theodorus): GeoGebra
• Goal Free Problems
  • Higher Number set Q19 (original questions)
• Go Teach Maths
  • Simplifying Surds
• MathsPad
  • Is it rational?✦
• Ticktock Maths
  • Simplifying Surds lesson (slides)

Worksheets

• Dr Austin Maths
  • Or Not ? (Word | PDF | Answers)
  • Prime Factors Fill In The Blanks (Word | PDF | Answers)
  • Introducing Practice Grid (Word | PDF | Answers)
  • Or Not Activity (Word | PDF | Answers)
  • More Practice Grid (Word | PDF✦ | Answers✦)
• Corbettmaths
  • Surds Practice Questions (Q1-4 & Q6-9) & Solutions
  • Surds Worksheet (Q1-10) & Solutions
• Maths 4 Everyone
  • Equivalent Surds First Steps
  • Adding and Subtracting Surds First Steps
  • Multiplying and Dividing Surds First Steps
• Miss Konstantine (MathsHKO)
  • Surds (Area and Prime Factors)✦
• Access Maths
  • True or False RAG Sheets
• MME
  • Surds Basics (exam style): Questions | Answers
• MadAsMaths (T. Madas)
  • Surds Q1–3 · questions only
• @taylorda01
  • Simplify using surds✦
• Mr Morley Maths
  • Simplifying Surds: Notes jotter/worksheet · Exam questions · Mark scheme
• Pret Homework (@teacherandy78)
  • Surds (@teacherandy78, pptx)

Dr Frost Video

Key Skill – Simplify a Surd

K673: Simplify a Surd.

Key Skill – Add or subtract surds with the same number under the square root.

K678: Add or Subtract Surds With the Same Number Under the Square Root.

Key Skill – Add or subtract surds that require simplifying.

K679: Add or Subtract Surds that Require Simplifying.

Key Skill – Simplify a multiple of a surd.

K674: Simplify a Multiple of a Surd.

Dr Frost Slides & Activities

Dr Frost Slides (1-4 & 10)

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 334a: Simplify a surd.
• 334b: Simplify a multiple of a surd.
• 334c: Write a surd in the form √a
• 334d: Simplify a surd of a fraction or mixed number.
• 336a: Add or subtract surds with the same root.
• 336b: Add or subtract surds that require simplifying.
• 336c: Reason about the sum, difference and product of a mixture of rational and irrational numbers.
• 334: Exam Practice: Simplifying surds
• 336: Exam Practice: Adding and subtracting surds

Activities & Resources

• Maths 4 Everyone
  • Pythagoras with Surds Loop: Set 1 · Set 2

Tutorial Videos

Surds Addition – Corbettmaths

Corbett Maths Surds Addition

Surds expanding brackets – Corbettmaths

Corbett Maths Surds Expanding Brackets

Online Platforms (with Videos & Exercises)

Activities

• Andy Lutwyche
  • GSCE Maths: Worksheet
  • Exploding
  • (Expanding Brackets) Codebreaker
  • Adding and Subtracting Codebreakers
  • Identities Codebreaker
  • Manipulating
• Math = Love (Sarah Carter)
  • Like Radicals Card Sort
  • Multiplying Surds Practice Book
  • Adding & Subtracting Surds Book
  • Operations with Surds Foldable
  • Operations with Surds Question Stack
  • Multiplying Surds Square Puzzle
  • Dividing Surds Organiser
  • Adding & Subtracting Surds Organiser
  • Multiplying Surds Organiser
• Desmos
  • Operations with Radicals Matching
• Don Steward
  • Grid Rectangles
  • Surd Multiplications and Powers
  • Powers of Phi
  • Eudoxus' Ladder
• Transum
  • Pythagoras with Surds
• Goal Free Problems
  • Higher Number set Q2 (original questions)
• Go Teach Maths
  • Multiplying & Dividing Surds
  • Adding & Subtracting Surds
  • Expanding Brackets With Surds
  • Pythagoras’ Theorem With Surds
• MathsPad
  • Multiplication squares✦
• Dr Austin Maths
  • Multiplying and Dividing Surds Decode the Joke✦ (answers✦)
• Ticktock Maths
  • Surds and Brackets lesson (slides)

Worksheets

• Dr Austin Maths
  • Square Numbers Fill In The Blanks (Word | PDF | Answers)
  • Multiplying and Dividing Crack the Code (Word | PDF | Answers)
  • Multiplying and Dividing Decode the Joke (Word | PDF | Answers)
  • Multiplying, Dividing Practice Grid(Word | PDF | Answers)
  • Manipulating Practice Strips (Word | PDF | Answers)
  • Manipulating Practice Grid (Word | PDF | Answers)
  • Expanding Brackets Practice Strips (Word | PDF | Answers)
  • Problem Solving Practice Strips (Word | PDF | Answers)
  • Adding and Subtracting Practice Strips (Word | PDF | Answers)
  • Algebra Practice Strips (Word | PDF | Answers)
  • Perimeter, Area and Volume Practice Strips (Word | PDF | Answers)
• Corbettmaths
  • Surds Practice Questions (Q5) & Solutions
  • Surds Worksheet (Q11-15) & Solutions
• Maths 4 Everyone
  • Multiplying Two-Part Surds Strengthen
• Pixi Maths
  • Simplifying Surds RAG
• Physics & Maths Tutor
  • Expressions Involving Surds and Algebraic Fractions: Notes · Worksheet · Solutions
• Access Maths
  • Ratios with Surds: Sheet 1✦ | Sheet 2✦
  • Surds Basic Calculations GSB Worksheet (with Answers)
• MME
  • Surds 1 (drill): Questions | Answers
• 1st Class Maths
  • Surds and Brackets✦ (answers✦)
• MadAsMaths (T. Madas)
  • Surd Exam Questions✦ Q1–2, 4–8, 10–11, 13, 15, 19, 23, 29, 32 (difficulty 2–3 of 5)
  • Surds Q6–23 · questions only
• @taylorda01
  • Expanding brackets with surds✦
• Starting Points Maths
  • Multiplication of Surds Build Up · PDF

Dr Frost Video

Key Skill – Multiply two surds.

K675: Multiply Two Surds.

Key Skill – Multiply two surds that require simplifying.

K676: Multiply Two Surds That Require Simplifying.

Key Skill – Divide two surds.

K677: Divide Two Surds.

Key Skill – Expand a single bracket with surds.

K680: Expand a Single Bracket With Surds.

Key Skill – Expand two brackets involving surds in the form (a + √b)(c + √b).

K681: Expand Two Brackets Involving Surds in the Form (a+rt(b))(c+rt(b)).

Key Skill – Expand two brackets with surds, where subsequent simplification of surds required.

K682: Expand Two Brackets With Surds, Where Subsequent Simplification of Surds Required.

Key Skill – Expand two brackets involving multiples of surds.

K683: Expand Two Brackets Involving Multiples of Surds.

Key Skill – Square a bracket involving surds.

K684: Square a Bracket Involving Surds.

Dr Frost Slides & Activities

Dr Frost Slides (5)

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 335a: Multiply two surds or a surd and a non-surd.
• 335b: Square a surd.
• 335c: Multiply multiples of surds.
• 335d: Square a multiple of a surd.
• 335e: Multiply two surds that require simplifying.
• 335f: Raise a surd to a positive integer power greater than 2.
• 335g: Divide two surds.
• 335h: Divide two surds that require simplifying.
• 335i: Multiply or divide surds with algebra.
• 337a: Expand a single bracket with surds.
• 337b: Expand a single bracket with surds, where simplification of surds is required.
• 337c: Expand two brackets involving surds given in the form (a+√b)(c+√b)
• 337d: Expand two brackets with surds, where simplification of surds is required.
• 337e: Expand two brackets involving multiples of surds.
• 337f: Square a bracket involving surds.
• 337g: Multiply three brackets involving surds.
• 337h: Compare coefficients of surds and non-surds to determine values of variables.
• 335: Exam Practice: Multiplying and dividing surds
• 337: Exam Practice: Expanding brackets with surds

Tutorial Videos

Rationalising denominators – Corbettmaths

Corbett Maths Rationalising Denominators (Up to 1:48)

Online Platforms (with Videos & Exercises)

Activities & Resources

• Pixi Maths
  • Rationalising Surds ppt
• Andy Lutwyche
  • Clumsy Clive
  • Defuse the Bomb
• Math = Love (Sarah Carter)
  • Why Rationalise the Denominator notes
  • Rationalising Question Stack
  • Rationalising Practice Book
  • Rationalising Notes
• Go Teach Maths
  • Rationalising Denominators: Without Using Conjugates
• BossMaths
  • N8b Surds
• Ticktock Maths
  • Rationalising the Denominator lesson (slides)

Worksheets

• Dr Austin Maths
  • The Denominator Fill In The Blanks (Word | PDF✦ | Answers✦) 
  • The Denominator Practice Strips (Word | PDF | Answers)
  • The Denominator Crack the Code (Word | PDF | Answers)
• Corbettmaths
  • Surds Worksheet (Q16) & Solutions
• MME
  • Rationalising & Harder Surds (exam style): Questions | Answers
• @taylorda01
  • Rationalise the denominator✦
• 1st Class Maths
  • Rationalise the denominator exam-style questions✦ (answers✦)
• MadAsMaths (T. Madas)
  • Surds Q4–5 · questions only
• Starting Points Maths
  • Rationalising the Denominator · PDF
• Mr Morley Maths
  • Rationalise the Denominator: Notes jotter/worksheet · Exam questions · Mark scheme

Dr Frost Video

Key Skill – Rationalise the denominator of a fraction where the denominator is a single surd.

K685: Rationalise the Denominator of a Fraction Where the Denominator is a Single Surd.

Dr Frost Slides & Activities

Dr Frost Slides (7-12)

Topic Tests

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 392a: Rationalise the denominator of a fraction given in the form fraca√b
• 392b: Rationalise the denominator of a fraction given in the form fracab√c
• 392c: Rationalise the denominator of a fraction given in the form fraca√b and where subsequent simplification is required.
• 392d: Rationalise the denominator of a fraction given in the form fraca√bc√d
• 392e: Simplify expressions given in the form fraca + √b√c
• 392f: Rationalise the denominator of a fraction to subsequently add or subtract surds.
• 392g: Solve equations given in the form (a√b)x = c or (a√b)x = c√d
• 392h: Simplify ≤ft(fraca√bright)ⁿ where n is large.
• 392: Exam Practice: Rationalising the denominator where the denominator consists of a single surd term

Tutorial Videos

Rationalising denominators – Corbettmaths

Corbett Maths Rationalising Denominators (Up to 1:48)

Online Platforms (with Videos & Exercises)

Activities

• Pixi Maths
  • Rationalising Surds ppt
• Math = Love (Sarah Carter)
  • Conjugates Notes
• Acute Learning Problem Pairs
  • Level 2 FM: Surds as PowerPoint or PDF
• Go Teach Maths
  • Rationalising Denominators Using Conjugates

Worksheets

• Dr Austin Maths
  • The Denominator Fill In The Blanks (Word | PDF✦ | Answers✦) 
  • The Denominator Practice Strips (Word | PDF | Answers)
  • The Denominator Proof Practice Strips (Word | PDF | Answers)
• Corbettmaths
  • Surds Worksheet (Q17) & Solutions
• Maths 4 Everyone
  • Rationalising the Denominator First Steps
• Pixi Maths
  • Rationalising the Denominator RAG
• Access Maths
  • Rationalising Surd Problems (Fractional)✦
• MME
  • Surds Hard (drill): Questions | Answers
• MadAsMaths (T. Madas)
  • Surd Exam Questions✦ Q3, 9, 12, 14, 17–18, 21, 24–25, 33, 37–38 (difficulty 2–3 of 5)
  • Surds Q24–33 · questions only

Dr Frost Video

Key Skill – Rationalise the denominator of a fraction in the form (a + √b)(c + √d).

K686: Rationalise the Denominator of a Fraction in the Form (a+rt(b))/(c+rt(d)).

Key Skill – Rationalise the denominator of a fraction in the form (a+b√c)(d+e√c).

K687: Rationalise the Denominator of a Fraction in the Form (a+b*rt(c))/(d+e*rt(f)).

Dr Frost Slides & Activities

Dr Frost Slides (13)

Topic Test

• Advanced Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 393a: Rationalise the denominator of a fraction given in the form fracab + √c
• 393b: Rationalise the denominator of a fraction given in the form fraca√bc + √d
• 393c: Rationalise the denominator of a fraction given in the form fraca√b + √c or fraca√b√c + √d
• 393d: Rationalise the denominator of a fraction given in the form fracab + c√d or fraca√bc + d√e
• 393e: Rationalise the denominator of a fraction given in the form fraca + √bc + √b
• 393f: Rationalise the denominator of a fraction given in the form fraca+√bc+√d, where simplification of a surd is required.
• 393g: Rationalise the denominator of a fraction given in the form fraca + b√cd + e√c
• 393h: Rationalise the denominator of a fraction given in the form fraca+b√cd+e√f, where simplification is required.
• 393i: Rationalise the denominator of a fraction where either the numerator or the denominator is squared.
• 393j: Solve equations given in the form x(a + b√c) = d or x(a + b√c) = d+e√f
• 393k: Solve equations with surds and unknowns on both sides.
• 393: Exam Practice: Rationalising the denominator where the denominator consists of a surd and a second term

Further Practice

• Practise Questions

Acute Learning Problem Pairs

• Surds (Algebra set) as PowerPoint or PDF
• Surds (Number set) as PowerPoint or PDF

Worksheets

• Dr Austin Maths
  • Revision Practice Grid (Word | PDF | Answers)
• Corbettmaths
  • Surds Practice Questions & Solutions
  • Surds Worksheet & Solutions
• Maths 4 Everyone
  • Surds Topic Review
  • Surds GCSE Questions and Solutions
• MathedUp
  • Surds: Worksheet · Practice · Quiz · Question Gallery
  • Surds & Indices: Worksheet · Practice · Quiz · Question Gallery
• Maths Genie
  • Surds: Booklet · Worksheet · Solutions · Lesson · Topic page
• Mathsaurus (Kevin Olding)
  • Surds (exam questions)
• Physics & Maths Tutor
  • Exact Values and Surds: Notes · Worksheet · Solutions
• crashMATHS
  • Laws of indices & surds worksheet
• Access Maths
  • Surds Complete Fluency & Reasoning Sheet
• @taylorda01
  • Using surds✦ (answers✦)
• Dr Frost
  • Surds Full Coverage GCSE Questions✦
• 1st Class Maths
  • Calculating with surds exam-style questions✦ (answers✦)
• MathsPad
  • Surds and rectangles worksheet✦

Activities

• Intervention Tasks
  • Find the Mistake + Your Turn to Try (PDF)
• NRICH (student problems)
  • Powers & Roots (Age 11-16): Problems
  • Powers & Roots (Age 11-16): Short Problems
• Don Steward
  • Square Roots of Surds
• Transum
  • Surds
• Interactive Maths
  • Surds: QQI | 10QQI | Count Down | Relay | Bingo
  • Surds: Worksheets
• Go Teach Maths
  • Manipulating Surds
  • Indices & Surds
• Oak National Academy
  • Surds Lessons and Resources✦
• MathsPad
  • Surds Odd One Out✦
• jhturner
  • Surds – Applying and problem solving✦
• Mathematics Assessment Project
  • Evaluating Statements about Radicals✦
• Interwoven Maths
  • Averages with surds✦ (by Nathan Day)
• Dr Austin Maths
  • Surds✦
  • Rationalising the denominator task✦

External

• NCETM
  • NCETM KS4 Mastery PD: 7.2 Using structure to transform and evaluate expressions (fractions, indices, surds) (PDF) · Solutions