Theory question 102
SurdsWithout using Mathematical Tables or a Calculator, simplify
(a) √50 − 3√2(2√2 − 5) − 5√32
(b) ½ log10(25/4) − 2log10(4/5) + log10(320/125)
Show the model answer
Model answer
(a) √50 = 5√2; 3√2(2√2 − 5) = 12 − 15√2; 5√32 = 20√2.
5√2 − 12 + 15√2 − 20√2 = −12.
(b) ½ log(25/4) = log(5/2); 2 log(4/5) = log(16/25).
log[(5/2) × (25/16) × (320/125)] = log 10 = 1.
Explanation
Turn coefficients into powers, then combine into one log.