To simplify the expression √71x, we need to find the largest perfect square factor of 71x. The prime factorization of 71 is 71 = 1 x 71 or 71 x 1, so 71 is a prime number and has no perfect square factors other than 1. Therefore, the largest perfect square factor of 71x is x itself.
To find the value of x that must be further simplified, we need to find the values of x that are perfect squares. We can do this by testing each of the answer choices:
√71(6) = 26.16... not a perfect square
√71(12) = 36.98... not a perfect square
√71(19) = 46.91... not a perfect square
√71(32) = 65.2... not a perfect square
√71(34) = 67.28... not a perfect square
√71(41) = 77.12... not a perfect square
√71(48) = 88.83... not a perfect square
None of the values of x result in a perfect square, so we cannot further simplify the expression √71x. Therefore, the answer is: None of the above (None of the values of x given require further simplification of the expression).