Carefully consider and answer the following questions. Suppose someone claims that ⌊ 3 √ 82 ⌋ = 4 . How would you verify whether ⌊ 3 √ 82 ⌋ = 4 using powers of 4 and powers of 5? Is ⌊ 3 √ 82 ⌋ = 4 ? Suppose that n, r, and root denote integer values where n ≥ 0 and r > 0. Further, suppose that ( root ) r ≤ n < ( root + 1 ) r . Can we conclude that root = ⌊ r √ n ⌋ ? Carefully justify your answer. Suppose that n and r denote integer values where n ≥ 0 and r > 0. Further, suppose you would like to know ⌊ r √ n ⌋ . When finding ⌊ r √ n ⌋ by a guess and verify method, is there any reason to try a guess, say g, where g < 0? Explain your answer. Similarly, is there any reason to try a guess g where g > n? Explain. Again, suppose that n and r denote integer values where n ≥ 0 and r > 0. What are two "simple" values, say lowEnough and tooHigh, such that lowEnough ≤ ⌊ r √ n ⌋ < tooHigh. Explain based on your answer to the previous question. Suppose you would like to know ⌊ 5 √ 47226 ⌋ . Explain how you could find ⌊ 5 √ 47226 ⌋ using a guess and verify method. Note: Explain your answer by relating this problem to the number guessing game described earlier. Think about what would be an appropriate question to use in place of "Is secret_number < guess_number?" and think about good choices for the starting values of lowEnough and tooHigh.