Again, suppose that n and r denote integer values where r > 0 and n ≥ 0. What are two "simple" values, say lowEnough and tooHigh, such that lowEnough ≤ ⌊n√r⌋⌊nr⌋ < tooHigh. Explain based on your answer to the previous question.

Suppose you would like to know ⌊47226−−−−−√5⌋⌊472265⌋. Explain how you could find ⌊47226−−−−−√5⌋⌊472265⌋ 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.

Answer explained

Explanation:

From the previous question we know that while searching for n^(1/r) we don't have to look for guesses less than 0 and greater than n. Because for less than 0 it will be an imaginary number and for rth root of a non negative number can never be greater than itself. Hence lowEnough = 0 and tooHigh = n.

we need to find 5th root of 47226. The computation of root is costlier than computing power of a number. Therefore, we will look for a number whose 5th power is 47226. lowEnough = 0 and tooHigh = 47226 + 1. Question that should be asked on each step would be "Is 5th power of number < 47227?" we will stop when we find a number whose 5th power is 47226.

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