Theory question 101
Number Bases(a) Given that 110x = 40five, find the value of x.
(b) Simplify 15/√75 + √108 + √432, leaving the answer in the form a√b, where a and b are positive integers.
Show the model answer
Model answer
(a) 110x = x2 + x and 40five = 20
x2 + x − 20 = 0, (x + 5)(x − 4) = 0
A base must be positive, so x = 4
(b) 15/√75 = 15/(5√3) = √3; √108 = 6√3; √432 = 12√3
Sum = 19√3
Explanation
Change both numbers to base ten; reject the negative root because a base is a positive whole number.