MYTUTOR SUBJECT ANSWERS

677 views

Express 4/(2-√2) in the form a+b√2 and write down the values of a and b.

This is a typical exam question which some students may find confusing.

The trick to this question is realising that you have to rationalise the denominator. (Topic: Surds)

4/(2-√2) = 4/(2-√2) x (2+√2)/(2+√2)

To rationalise, you multiply both the top and the bottom by the conjugate of the denominator. In simple terms, the conjugate is the same as the denominator but with the opposite sign. you are essentially multiplying by 1 so you haven’t actually changed the expression.

= 4(2+√2) / (2-√2)(2+√2)

= (8+4√2) / (4 + 2√2 -2√2 -2)

= (8+4√2) / (4-2)

 As you can see, this has removed the complicated square root from the denominator which makes it easier to simplify.

= 8/2 + (4√2)/2

=4 + 2√2

The rest is simple calculation to get the form the question asks for. So…

a = 4, b = 2

William A. GCSE Maths tutor, A Level Maths tutor

1 year ago

Answered by William, a GCSE Maths tutor with MyTutor


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

521 SUBJECT SPECIALISTS

£18 /hr

Josie O.

Degree: Geography (Bachelors) - Edinburgh University

Subjects offered:Maths, Science+ 3 more

Maths
Science
Geography
Chemistry
-Personal Statements-

“Geography student with a passionate interest in human/environment interactions. I'm a friendly and experienced tutor, currently open for more students!”

£18 /hr

Melissa P.

Degree: Mathematics (Bachelors) - Birmingham University

Subjects offered:Maths, Spanish

Maths
Spanish

“About me:  I am currently studying for a Maths degree at the University of Birmingham. I have enjoyed Maths since I was very young and hope I can pass some of this on to you!  I am very friendly. I have been coaching gymnastics since...”

£36 /hr

Adam B.

Degree: Economics and Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Economics

“Hi!  I'm an enthuthiastic and motivated tutor with a commitment to developing my student's understanding of concepts within their chosen subjects.  As an Economics and Mathematics undergraduate I am committed to delivering a tailored...”

About the author

William A.

Currently unavailable: for new students

Degree: Computing (Masters) - Imperial College London University

Subjects offered:Maths

Maths

“You've taken the first step to find me so who am I? I'm a Computing student at Imperial College London. I like Maths. I like teaching. Put that all together and you've found what you're looking for! What I can do for you? Over 3 year...”

You may also like...

Other GCSE Maths questions

How do you change the subject of the formula?

Solve ((3x+2)/(x-1)) +3 =4

ABC is a right angled triangle. D is the point on AB such that AD = 3DB. AC = 2DB and angle A = 90 degrees. Show that sinC = k/√20 where k is an integer. Find the value of k

How do i solve a system of 2 equations?

View GCSE Maths tutors

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

mtw:mercury1:status:ok