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Corbett MathsSimplifying surds
Corbett MathsRationalising the denominator
GCSE Maths TutorSurds (Part 5) Rationalising the Denominator 1 - 10 Minute Maths Series | GCSE Maths Tutor
GCSE Maths TutorSurds (Part 2) Adding & Subtracting - 10 Minute Maths Series | GCSE Maths Tutor
Key facts & methods
Simplifying and manipulating surds — fill in the table
| Operation | Rule |
|---|
| Simplify | |
| Add/subtract | |
| Multiply | |
| Expand brackets | |
| Difference of two squares | |
Rationalising the denominator
- Goal: remove the surd from the denominator.
- Simple case: multiply top and bottom by √n. E.g. 1/√3 × √3/√3 = √3/3.
- Conjugate case: denominator is (a+√b). Multiply by (a−√b). E.g. 1/(2+√3) × (2−√3)/(2−√3) = (2−√3)/(4−3) = 2−√3.
- The denominator always becomes rational because (a+√b)(a−√b) = a²−b.
- Always simplify fully — check if the fraction can be reduced further.
Exam questions — 4 questions · 9 marks · Edexcel 4MA1 style
⚡ Show ALL working — the AI awards method marks just like a real examiner. Partial credit for correct working even if the final answer is wrong.
3 marksSimplify and expandGrade 7 Booklet Q1 ✏️ No calculator
Work out (5+√3)(5−√3) ÷ √22. Give your answer in simplest form. (3 marks)
Hint: (5+√3)(5−√3) is difference of two squares = 25−3. Then divide by √22. Simplify 22/√22 by rationalising or cancelling.
+30 XP
3 marksRationalise the denominatorGrade 7 Booklet Q2 ✏️ No calculator
(a) Rationalise the denominator of 1/√3. (b) Expand (2+√3)(1+√3). Give your answer in the form a+b√3 where a and b are integers. (3 marks)
Hint: (a) Multiply numerator and denominator by √3. (b) FOIL: First + Outer + Inner + Last. √3 × √3 = 3.
+30 XP
3 marksComplex surd problemGrade 7 Booklet Q7 ✏️ No calculator
Expand and simplify (2+√3)(7−√3). Give your answer in the form a+b√3 where a and b are integers. (3 marks)
Hint: FOIL: 2×7=14, 2×(−√3)=−2√3, √3×7=7√3, √3×(−√3)=−3. Collect integer terms and √3 terms separately.
+30 XP
1 markSimplify surd4MA1 style
Which of the following is √48 in its simplest form?
Quick recall flashcards
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