Express (3 - sqrt(5))^2 in the form m + n*sqrt(5), where m and n are integers.

Layout the problem in a more recognisable form such as (3 - sqrt(5))(3 - sqrt(5)). Notice that this looks a lot like a factorised quadratic equation, where sqrt(5) can be treated as a variable like x. Therefore, we can expand these brackets in the same way we expand these factorised quadratic equations. Following the same process should result in 9 - 6sqrt(5) + sqrt(5)2 which is equal to 14 - 6sqrt(5). Checking back with the question it where m and n are wanted, n = -6 as it is the coefficient of the term with sqrt(5) and m = 14 as it is the term that is a pure integer.

AP
Answered by Anselmo P. Maths tutor

8166 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How can I calculate the maximum value of the compound angle formulae Rsin(x+a) and Rcos(x+a)?


How to find the reciprocal of a graph, such as y=cos(x)?


How do you find the acute angle between two intersecting lines whos equations are given in vector form?


How can we determine stationary points by completing the square?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences