Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem23

Levels 9&10 Video Solutions 2010 problem23

Video Transcription

Video Summary

The video discusses how many numbers \( n \) from 1 to 100 satisfy that \( n^n \) is the square of a natural number. First, the video considers even numbers, where \( n/2 \) will still be a natural number, accounting for 50 candidates. Then it examines odd numbers, particularly those that are perfect squares. Five qualifying odd numbers (1, 9, 25, 49, 81) are identified. Combining these with the 50 even numbers gives a total of 55 numbers where \( n^n \) is a perfect square. Thus, the answer to the question is 55.

Keywords

perfect square

natural number

even numbers

odd numbers

n^n