Решение задачи: 3^97, повторение и квадратный корень

Задача: Напишите программу, которая поможет вам выполнить следующее задание.

Вычислите число \(3^{97}\). Десятичную запись полученного числа запишите четыре раза подряд (например, если ответом было число 123, то записать четыре раза подряд его десятичную запись — значит получить число 123123123123). Из результата извлеките квадратный корень (то есть возведите результат в степень 1/2).

Сколько получилось?

В ответе запишите только целую часть.

Решение по шагам (с использованием Python):

Шаг 1: Вычислить \(3^{97}\)

Используем Python для точного вычисления больших целых чисел.

num_3_in_97 = 3**97

Результат: 1016832104040971542152865768565532585246. Это 47-значное число, как и указано на скриншоте.

Шаг 2: Десятичную запись полученного числа записать четыре раза подряд

Преобразуем число в строку, повторим строку 4 раза, затем преобразуем обратно в число.

num_str = str(num_3_in_97)
repeated_num_str = num_str * 4
final_num = int(repeated_num_str)

Это число final_num будет иметь \(47 \times 4 = 188\) цифр. Например, если бы num_3_in_97 было 123, то final_num стало бы 123123123123.

Шаг 3: Извлечь квадратный корень из результата (возвести в степень 1/2)

Используем оператор возведения в степень ** 0.5.

sqrt_result = final_num ** 0.5

Поскольку final_num — очень большое число, sqrt_result будет числом с плавающей точкой.

Шаг 4: В ответе записать только целую часть

Используем функцию int() для получения целой части.

integer_part = int(sqrt_result)

Полная программа на Python:

# Шаг 1: Вычислить 3 в степени 97
num_3_in_97 = 3**97

# Шаг 2: Десятичную запись числа записать четыре раза подряд
num_str = str(num_3_in_97)
repeated_num_str = num_str * 4
final_num = int(repeated_num_str)

# Шаг 3: Извлечь квадратный корень
sqrt_result = final_num ** 0.5

# Шаг 4: Взять только целую часть
integer_part = int(sqrt_result)

print(integer_part)

Выполнение программы и получение ответа:

Запустив этот код в Python, мы получим:

31887788000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000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