Suppose you would like to know 472265472265. Explain how you could find 472265472265 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.

Assume you are given the power method specified as follows:

/**

* Returns {@code n} to the power {@code p}.

*

* @param n

* the number to which we want to apply the power

* @param p

* the power

* @return the number to the power

* @requires Integer.MIN_VALUE <= n ^ (p) <= Integer.MAX_VALUE and p >= 0

* @ensures power = n ^ (p)

*/

private static int power(int n, int p) {...}

Use your answers to the previous questions to implement the root method specified below. Be sure to use the idea of interval halving.

/**

* Returns the {@code r}-th root of {@code n}.

*

* @param n

* the number to which we want to apply the root

* @param r

* the root

* @return the root of the number

* @requires n >= 0 and r > 0

* @ensures root ^ (r) <= n < (root + 1) ^ (r)

*/

private static int root(int n, int r) {...}