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: http://www.bbc.co.uk/education/guides/z7fbkqt/revision/2

Factorise the equation x^2 + 5x+6 = 0

Related Maths GCSE answers

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

If 11 carrots weigh 170g how much would 20 carrots weigh?

Expand and simplify the following expression: x(5x – 2) – 3(x2 – 2x + 7)

A rectangle has an area of 20 cm^2. Its length and width are enlarged by scale factor 3. Find the area of the enlarged rectangle.

We're here to help

Company Information

Popular Requests

© MyTutorWeb Ltd 2013–2024

CLICK CEOP