i) Simplify (2 * sqrt(7))^2 ii) Find the value of ((2 * sqrt(7))^2 + 8)/(3 + sqrt(7)) in the form m + n * sqrt(7) where n and m are integers.

i) (2sqrt(7))2 = 2 sqrt(7)2 = 4 * 7 = 28      (1 mark) ii) First of all substitute the answer from above.    ((2 * sqrt(7))2 + 8) / (3 + sqrt(7)) = (28 + 8) / (3 + sqrt(7)) = 36 / (3 + sqrt(7)) Multiply by (3 - sqrt(7))/(3 - sqrt(7)) = 1.    36 / (3 + sqrt(7)) = 36 / (3 + sqrt(7)) * (3 - sqrt(7)) / (3 - sqrt(7)) = (36 * (3 - sqrt(7))) / ((3 + sqrt(7)) * (3-sqrt(7)) = (108 - 36 * sqrt(7)) / (9 + 3 * sqrt(7) - 3 * sqrt(7) - 7) = (108 - 36 * sqrt(7)) / 2 = 54 - 18 * sqrt(7).      (3 marks) (Hence m=54 and n=-18) 

Answered by Andrew B. Maths tutor

6854 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Prove that (1-cos2x)/sin(2x) = tan(x) where x ≠ nπ/2


State the conditions under which a binomial distribution can be approximated as a normal distribution, and state how the parameters needed would be calculated.


Find all the stationary points of the curve: y = (2/3)x^3 – (1/2)x^2 – 3x + 7/6 and determine their classifications.


Find the turning point(s) of the following function f(x) = x^2-2x+4. Determine whether the turning point is a minimum or maximum.


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