Theory question 106
Fractions, Decimals and Approximation(a) Without using mathematical table or calculator, evaluate: √((0.18 × 12.5)/(0.05 × 0.2)).
(b) Simplify: (8 − 4√18)/√50 leaving your answer in the a + b√n where a and b are rational numbers and n is an integer.
(c) x, y and z are related such that x varies directly as the cube of y and inversely as the square of z. If x = 108 when y = 3 and z = 4, find z when x = 4000 and y = 10.
Show the model answer
Model answer
(a) 0.18 × 12.5 = 2.25 and 0.05 × 0.2 = 0.01, so √225 = 15.
(b) √18 = 3√2 and √50 = 5√2: (8 − 12√2)/(5√2). Multiply by √2/√2: (8√2 − 24)/10 = −12/5 + (4/5)√2.
(c) x = ky3/z2: 108 = 27k/16, so k = 64.
4000 = 64 × 1000/z2, so z2 = 16 and z = 4.
Explanation
Rationalise the denominator by multiplying by √2/√2.