dividing square roots

6/28/2023

The problem looks simple, but the lesson readies a middle school student for algebra and is placed in the blog because John reviews must-know, pre-Algebra definitions. I have entered several of John’s videos into the blog because this is the ideal way to teach or tutor, unlike the vile teacher in the post, UK Teacher Recorded 6/24/2023.

You can divide the square root of 30 into 10 parts. It will be an approximation, but it's good enough.

3 Comments

Josef Ketzer

7/2/2023 06:32:28 am

Very interesting! And here's an math riddle, easy to solve with much time and diligence, but there should also exist an elegant formula:
Inside a large aisle-shaped room, there are lined up 100 light bulbs, each connected with a separate switch. In front of the room's entrance, a queue of 100 people is waiting in line. The first person enters and turns on every bulb, after him the second one turns out every second bulb, # 3 operates every third bulb (from here on, it can be switched on or off), # 4 operates every fourth, and so on. Finally the last person, the 100th, crosses the room, operates the switch only on the last, the 100th bulb, and leaves.
How many bulbs are lit after these proceedings 💡🤔❓

Robert E. Dunn link

7/3/2023 01:23:15 am

Factors come in pairs, except for perfect squares.

This means that a number has an odd number of factors if and only if it is a perfect square.

For example, nine has an odd number of factors, i.e., three: 1,3, and 9. For 16, there are five factors: 1, 2, 4, 8, and 16.

To determine how many light bulbs are illuminated after the 100th person has passed through the room, we need to count the number of bulbs that have an odd number of factors.

Again, this will be the perfect squares.

There are 10 perfect squares from 1 and 100: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

Therefore, the final number of illuminated bulbs is 10.

Joe: this is a ChatGPT answer!

Josef Ketzer

7/4/2023 11:48:45 am

Ah. that's very interesting. Thanks, Bobby!

dividing square roots

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