Final answer:
The operation involves square roots of decimals, which are converted into percentages, allowing for an easier square root calculation. After calculating these square roots, we perform the addition and subtraction, respectively, and then divide the results. The final answer is 15.
Step-by-step explanation:
The value of \(\sqrt{0.2304}\) + \(\sqrt{0.1764}\) \div \(\sqrt{0.2304}\) - \(\sqrt{0.1764}\) requires us to first find the square roots of the given decimals, which can be represented as percentages:
\(\sqrt{0.2304} = \sqrt{23.04\%} = 0.48\) and \(\sqrt{0.1764} = \sqrt{17.64\%} = 0.42\)
Substituting these values into the original expression:
0.48 + 0.42 / 0.48 - 0.42
Now we perform the operations maintaining the order, addition and subtraction:
0.48 + 0.42 = 0.90 and 0.48 - 0.42 = 0.06
Finally, we divide the results:
0.90 / 0.06 = 15
Therefore, the value of the original expression is (a) 15.