Theory question 102
Surds(a) Simplify 3√75 − √12 + √108, leaving the answer in surd form (radicals).
(b) If 124n = 232five, find n.
Show the model answer
Model answer
(a) 3√75 = 15√3, √12 = 2√3, √108 = 6√3. 15√3 − 2√3 + 6√3 = 19√3.
(b) 232five = 50 + 15 + 2 = 67. n2 + 2n + 4 = 67 → n2 + 2n − 63 = 0 → (n + 9)(n − 7) = 0. A base must be positive, so n = 7.
Explanation
Write each surd as a multiple of √3.