(a) Given that 110(_x) – 40(_{five}). find the value of x
(b) Simplify (frac{15}{sqrt{75}} – sqrt{432}), leaving the answer in the form a(sqrt{b}), where a and b are positive integers.
Explanation
(a) Conveting to bese ten and when simplified yielded x(^2) + x – 20 = 0 and when solves ; (x + 5)(x – 4) = 0
x = 4 or x = -5 But x cabbot be negative since it is the base, therefore, x = 4.
(b) Simplify (frac{15}{sqrt{75}}) = (frac{3}{sqrt{3}}) which will yield (sqrt{3}) when rationalized. Similarly, (sqrt{108}) = 6(sqrt{3}) and (sqrt{432}) = 12(sqrt{3}). Thus, substracting and simplifying will yield (sqrt{3} + 12sqrt{3} = 19sqrt{3})