Final answer:
The expression ¹⁸√10 cannot be simplified further as 10 is not a perfect power of any number. Therefore, it remains as ¹⁸√10 and does not match any of the provided options.
Step-by-step explanation:
The student asked for the simplified radical form of ¹⁸√10. To simplify this expression, we should understand the concept of radical expressions and how to manipulate them. The given expression is the 18th root of 10, which cannot be simplified further as 10 is not a perfect power of any number that could be extracted from the radical.
Therefore, there is no simpler radical form for this expression. None of the provided options a) √2, b) ¹⁸√100, c) ²⁰√18, or d) 180 can be considered as a simplified form of ¹⁸√10 as none of these represent the 18th root of 10.
Option a) is the square root of 2, option b) simplifies to 10 times the ninth root of 10 (which is not equal to the 18th root of 10), option c) is irrelevant as it represents the 20th root of 18, and option d) is simply the number 180, which has no relation to the original expression.