Value of $\sqrt{.01} \times \sqrt[3]{.008} - .02$ is

Concept & Logic Evaluate the square root and cube root of the decimal numbers individually, paying strict attention to the number of decimal places for each radical. After evaluating, apply BODMAS (Multiplication before Subtraction) to find the final numerical value. Step-by-Step Solution * **Given**: $$\sqrt{0.01} \times \sqrt[3]{0.008} - 0.02$$ * **Step 1: Evaluate the square root of $0.01$.** The number $0.01$ has $2$ decimal places. The square root will have $2 \div 2 = 1$ decimal place. Since $\sqrt{1} = 1$, the result is $0.1$. * **Step 2: Evaluate the cube root of $0.008$.** The number $0.008$ has $3$ decimal places. The cube root will have $3 \div 3 = 1$ decimal place. Since $\sqrt[3]{8} = 2$, the result is $0.2$. * **Step 3: Substitute back and simplify using BODMAS.** $$0.1 \times 0.2 - 0.02$$ * Perform the multiplication first. When multiplying $0.1$ and $0.2$, multiply the numbers ($1 \times 2 = 2$) and add the decimal places ($1 + 1 = 2$). $$0.1 \times 0.2 = 0.02$$ * Perform the final subtraction: $$0.02 - 0.02 = 0$$ Exam Strategy & Shortcut Quickly convert the decimals in your head to fractions to avoid decimal errors: $\sqrt{1/100} = 1/10$. $\sqrt[3]{8/1000} = 2/10$. Multiply them: $(1/10) \times (2/10) = 2/100 = 0.02$. Subtracting $0.02$ from $0.02$ is instantly $0$. Fraction conversion often prevents silly decimal placement mistakes. Common Pitfall Miscalculating the product of $0.1 \times 0.2$. Many students incorrectly write $0.2$ instead of $0.02$, leading them to calculate $0.2 - 0.02 = 0.18$, which isn't an option but causes panic and wasted time checking steps. Final Answer **Therefore, the correct answer is 0.**