Final answer:
The mixed number of √40 is 2√10 after factoring the number 40 and taking the square root of the perfect square within it. However, this result does not match any of the given options, which suggests there may be an error in the question or options provided.
Step-by-step explanation:
To find the mixed number of √40, we need to factor the number 40 into its prime factors to see if there is a perfect square within it that we can take the square root of separately. The factorization of 40 is 23 × 5 = 2 × 2 × 2 × 5. We see that 22 (which is 4) is a perfect square. So we take out the square root of 4 and leave the rest inside the square root.
√40 = √(4 × 10) = √4 × √10 = 2 × √10, which gives us a mixed number of √40 as 2√10.
However, none of the options A) 3√10, B) 4√5, C) 5√2, D) 6√2 match our answer, suggesting a potential mistake in the options or the question itself. In such a case, we should double-check our calculations and if they're indeed correct, raise the issue with the instructor for clarification.