Theory question 101
Surds(a) Express 2√2/(√48 − √8 − √27) in the form p + q√r, where p, q and r are rational numbers.
(b) If V = A log10(M + N), express N in terms of M, V and A.
Show the model answer
Model answer
(a) √48 = 4√3, √8 = 2√2, √27 = 3√3, so the denominator is √3 − 2√2
Multiply top and bottom by √3 + 2√2: denominator 3 − 8 = −5, numerator 2√6 + 8
= −8/5 − (2/5)√6, i.e. p = −8/5, q = −2/5, r = 6
(b) log10(M + N) = V/A
M + N = 10V/A
N = 10V/A − M
Explanation
Simplify each surd first, then rationalise with the conjugate.