$\sqrt{24 \div 0.5 + 1} + \sqrt{18 \div 0.6 + 6} = $ $x$

Concept & Logic This problem tests your ability to apply the BODMAS rule (specifically handling division with decimals) inside radical expressions. You must completely simplify the expressions under each square root before adding them together. $$ \sqrt{a} + \sqrt{b} \neq \sqrt{a+b} $$ Step-by-Step Solution * **Given:** $\sqrt{24 \div 0.5 + 1} + \sqrt{18 \div 0.6 + 6} = x$ * **Calculation:** First, evaluate the expression inside the first square root: $24 \div 0.5 = 24 \div \frac{1}{2} = 24 \times 2 = 48$ $48 + 1 = 49$ So, the first term is $\sqrt{49} = 7$. * Next, evaluate the expression inside the second square root: $18 \div 0.6 = \frac{180}{6} = 30$ $30 + 6 = 36$ So, the second term is $\sqrt{36} = 6$. * Finally, add the simplified terms: $7 + 6 = 13$ Exam Strategy & Shortcut Division by a decimal like 0.5 is exactly the same as multiplying by 2. Division by 0.6 is the same as multiplying by $\frac{10}{6}$. Recognizing these fraction equivalents allows you to do the math mentally: $24 \times 2 = 48$, and $18 \times \frac{10}{6} = 30$. This skips the need for long division. Common Pitfall A frequent mistake is adding the numbers inside the roots before performing the division, or incorrectly evaluating $18 \div 0.6$ as $3$ instead of $30$ due to decimal misplacement. Always align your decimal points carefully! Final Answer **Therefore, the correct answer is 13.**