MYTUTOR SUBJECT ANSWERS

1813 views

Simplify (7+sqrt(5))/(sqrt(5)-1), leaving the answer in the form a+b*sqrt(5)

Step 1 - Identify the difference between the required form of the answer and the expression to be simplified: 

It can be seen that in order to simplify the expression we need to somehow get rid of the denominator.

Step 2 - Attempt a method to get rid of the denominator: 

The best way to get rid of the denominator is to multiply it by (sqrt(5)+1). In order to keep the expression the same we must do the same to the numerator as well. 

This gives us,

((7+sqrt(5))/(sqrt(5)-1))*((sqrt(5)+1)/(sqrt(5)+1))

Step 3 - Carry out the necessary calculations:

The top parts of the fractions multiply together and the bottom parts of the fractions multiply together.

For the top part this gives us,

(7+sqrt(5))*(sqrt(5)+1) = 7*sqrt(5)+7+5+sqrt(5)

= 8*sqrt(5)+12

For the bottom part this gives us,

(sqrt(5)-1)*(sqrt(5)+1) = 5+sqrt(5)-sqrt(5)-1 = 4

Dividing the top part by the bottom part gives us,

2*sqrt(5)+3

Step 4 - Check that the answer is in the correct form.

The question asks for an answer in the form,

a+b*sqrt(5)

Our answer can be written in this format with a = 3 and b = 2.

Ian R. GCSE Maths tutor, GCSE Physics tutor, Uni Admissions Test -Per...

2 years ago

Answered by Ian, an A Level Maths tutor with MyTutor


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

354 SUBJECT SPECIALISTS

£24 /hr

Ed W.

Degree: Medicine (Bachelors) - Edinburgh University

Subjects offered:Maths, Further Mathematics + 3 more

Maths
Further Mathematics
Chemistry
Biology
-Medical School Preparation-

“Hi! I'm Ed and I'm currently studying Medicine at the University of Edinburgh. I tutor at GCSE and A Level forBiology, Chemistry and Maths, and at GCSE level forFurther Maths. These are subjects I'm very comfortable in and enjoy. With ...”

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

£20 /hr

Alicia P.

Degree: Maths and Economics (Bachelors) - Leeds University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
-Personal Statements-

“Maths and Economics Student from Uni of Leeds. Very friendly with previous experience of working with and teaching younger people.”

MyTutor guarantee

|  3 completed tutorials

About the author

Ian R.

Currently unavailable: until 01/09/2016

Degree: MSc International Development (Masters) - Edinburgh University

Subjects offered:Maths, Science+ 1 more

Maths
Science
Physics

“My name is Ian and I am an experienced tutor specialising in Maths, Physics and English as Foreign language. I am currently a Masters student at the University of Edinburgh studying International Development My previous studies includ...”

MyTutor guarantee

|  6 completed tutorials

You may also like...

Other A Level Maths questions

Use the chain rule to differentiate y=1/x^2-2x-1

Solve x^2 + 8x +3 = 0 by completing the square.

What is the difference between a tangent and a normal?

How to solve a quadratic equation?

View A Level 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