Express (7+ √5)/(3+√5) in the form a + b √5, where a and b are integers.

(7+ √5)/(3+√5)Here, the denominator is not rational - (numbers like 2 and 3 are rational). A number with an irrational denominator isn't incorrect, it just isn't in the simplest form it can be in.To rationalise the denominator in this case, we want to use the denominator's conjugate (e.g. Conjugate of 2-√3, would be 2+√3)We do this because it helps remove the surd from the denominator.(7+ √5)/(3+√5) * (3-√5) /(3-√5) (Note that the second part - (3-√5) /(3-√5) - we use this because anything divided by itself equals 1. Multiplying anything by 1 doesn't change it's value)Multiplying fractions (toptop and bottombottom): (7+ √5)(3-√5)/(3+√5)(3-√5) Use FOIL to multiply out brackets and simplify---> 4-√5So, a=4 and b=-1

OG
Answered by Oscar G. Further Mathematics tutor

17356 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

Given a^2 < 4 and a+2b = 8. Work out the range of possible values of b. Give your answer as an inequality.


In a chess club there are x boys and y girls. If ten more boys join and one more girl joins, there is an equal amount of boys and girls. Knowing that y = 2x+2, Calculate x and y. [4 marks]


Why is it that when 'transformation A' is followed by 'transformation B', that the combined transformation is BA and not AB?


Consider the Matrix M (below). Find the determiannt of the matrix M by using; (a) cofactor expansion along the first row, (b) cofactor expansion along the second column


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