1484 views

### Show clearly that (3√3)^2 = 27

Show clearly that (3√3)2 = 27

First of all, the question looks overfacing due to the surds, I can assure you that surds are not scary, they simply act as a means of clearing up messy numbers such as 1.73205 08075 68877 29352 74463... (carries on for a billion digits) which can be simply written as √3!

So, how would we work out (3√3)without using a calculator? Well, luckily the question tells us that the answer we need to find is 27, so we can't go far wrong within these parametres.

First of all, (3√3)2  is a tidy and mathematical way of writing 3√3 x 3√3.

A surd is not an equation, it is just a tidy way of writing a messy number.

Remember the rule of surds:

√(a x b) is the same as √a x √b...

3√3 is a tidy, surdy way of writing √3x √3. Which is the same as √9 x √3... √(9 x 3).... which can also be written as √27.

so, what we have to show is that √272= 27.

√27 x √27= 27, because, by timesing together two like surds, we can get rid of the root sign because, in general, multiplying two like surds gives a rational number... (√a x √a= a) (2√a x √a=2a)

Hence, we have just proved that (3√3)2= 27 simply by referring to the basic rules of surds :)

2 years ago

Answered by Eleanor, a GCSE Maths tutor with MyTutor

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

#### 643 SUBJECT SPECIALISTS

£24 /hr

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.”

£30 /hr

Degree: Law (Bachelors) - Durham University

Subjects offered:Maths, Business Studies+ 2 more

Maths
.LNAT.
-Personal Statements-

“Durham law graduate with four years tutoring experience in a wide range of subjects. ”

£24 /hr

Degree: Biological Sciences (Biochemistry) (Bachelors) - Edinburgh University

Subjects offered:Maths, Mandarin+ 2 more

Maths
Mandarin
Chemistry
Biology

Currently unavailable: for new students

Degree: History (Bachelors) - Durham University

Subjects offered:Maths, History+ 5 more

Maths
History
Extended Project Qualification
English Literature
English Language
-Personal Statements-

“ABOUT ME I am about to start my final year of my BA in History at Durham University.  I absolutely adore my subject, having studied a great wealth of topics and periods, both British and worldwide. Currently, I am setting to work on m...”

### You may also like...

#### Other GCSE Maths questions

if x^2 + 9x + 20 = 0, what are the possible values of x?

3x^2 + 7x - 13 = 0. What is x?

Write y = x^2 + 4x + 6 in the form y = (x + a)^2 + b. What is the minimum value of y?

Each day Chen buys pasta or a sandwich. Where Pasta costs £3.20 and Sandwich costs £2.75. For 45 days, the relative frequency of Chen buying a sandwich was one fifth. Altogether, how much did he pay?

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