Rationalise the denominator of the following fraction: 1/(√2 + 1)

We start with 1/(√2 + 1) 

Normally with rationalising surd denominators we multiply the top and bottom of the fraction by the denominator. But this time we have a surd ADDED by a rational number. 

In this case we multiply the top and bottom by the denominator with the connecting + or - sign REVERSED ie by:(√2 - 1)

So we get

(√2 - 1) / (√2 + 1)(√2 - 1) 

The bottom is multiplied out like a quadratic... a special type of quadratic [(a - b)(a + b)]. A handy but not vital rule to remember is:

(a - b)(a + b) = a2 - b2 

So back to our fraction, we get

(√2 - 1) / (2 - √2 + √2 - 1)

= (√2 - 1) / (2 - 1)   

= (√2 - 1) / 1

= √2 - 1 --> our final answer!

If you would like more examples, as usual BBC Bitesize is good at walking through the solutions to a number of types of questions on surds: 

Richard M. GCSE Italian tutor, GCSE Geography tutor, GCSE History tut...

3 months ago

Answered by Richard, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


Katja H. IB Geography tutor, GCSE Geography tutor, GCSE English tutor...
View profile
£18 /hr

Katja H.

Degree: MA Geography and Politics (Bachelors) - Glasgow University

Subjects offered: Maths, Geography+ 3 more


“I'm a student of Geography and Politics at Glasgow Univeristy. I have always loved Geography and believe that studying it is like studying for a degree in interesting conversations :)My experience tutoring also includes Biology, Fren...”

Joshua B. GCSE Maths tutor, A Level Maths tutor, A Level Further Math...
View profile
£18 /hr

Joshua B.

Degree: Mathematics (Masters) - Durham University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“About me: Hi! I’m Josh, a second year at Durham University on a four-year Mathematics course. I’ve always loved Maths, and I’ve always excelled at it, too. I got100% in both my Maths IGCSE and A-Level. Not only did I do Further Maths,...”

Andy C. GCSE Maths tutor, A Level Maths tutor
View profile
£18 /hr

Andy C.

Degree: Maths and Philosophy (Bachelors) - Bristol University

Subjects offered: Maths


“Second year Maths and Philosophy student at Bristol. Looking to tutor Maths GCSE”

MyTutor guarantee

About the author

Richard M. GCSE Italian tutor, GCSE Geography tutor, GCSE History tut...
View profile
£18 /hr

Richard M.

Degree: Philosophy, Politics and Economics (Bachelors) - Oxford, Keble College University

Subjects offered: Maths, Italian+ 7 more

Government and Politics
English Literature
English Language
.TSA. Oxford.
-Personal Statements-

“About Me and My Teaching: I am a Philosophy, Politics and Economics student at Keble College, Oxford. From October I'll be specialising in Politics and Economics. I love understanding how the human world works and as such I am always ...”

MyTutor guarantee

You may also like...

Posts by Richard

Rationalise the denominator of the following fraction: 1/(√2 + 1)

With the use of examples, explain how physical factors can hinder a country's development

Other GCSE Maths questions

Find the zeroes of the quadratic polynomial x^2 + 8x + 15.

Show clearly that (3√3)^2 = 27

Given that your grade for your computing is based on 5 coursework that weigh differently, and you know the results of 4: 80, 75, 50 and 90 which weighs 10%, 20%, 45% and 5%. What grade do you need in your last coursework to achieve at least a B (70%)?

How do i factorise 20 + 10x?

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss