You do not need to show your working or reasoning in this question. (a) Let $a = 75 = 3 \cdot 5^2$. (i) Find the least positive integer $b$ such that $\sqrt{5}(a + b) = 0$. (ii) Find the least positive integer $b$ such that $\sqrt{5} (a + b) = 1$. (iii) Find the least positive integer $b$ such that $\sqrt{5}(a + b) = 2$. (iv) Find the least positive integer $b$ such that $\sqrt{5} (a + b) = 3$. (b) Repeat part (a) with $a = 100 = 4 \cdot 5^2$ instead.
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