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

17015 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

If the equation of a curve is x^2 + 9x + 8 = y, then differentiate it.


f(x) = 2x^3+6x^2-18x+1. For which values of x is f(x) an increasing function?


A curve has equation: y = x^3 - 3x^2 + 5. Show that the curve has a minimum point when x = 2.


Differentiate y = x*cos(2x)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences