Explained how you show your class how to work on the square root of729 using the averaging method ?

To demonstrate how to work on the square root of 729 using the averaging method, I would first explain the concept of square roots to the class. I would explain that the square root of a number is a value that, when multiplied by itself, gives the original number.

Next, I would show the class how to use the averaging method to find the square root of 729. The averaging method involves finding two numbers that, when multiplied together, equal the original number. In this case, we are looking for two numbers that multiply to 729.

I would start by finding the square root of a number close to 729, such as 700. The square root of 700 is approximately 26.46. Next, I would find the square root of a number close to 729 on the other side, such as 800. The square root of 800 is approximately 28.28.

I would then average these two numbers by adding them together and dividing by 2. This would give us (26.46 + 28.28) / 2 = 27.37. This is our initial estimate for the square root of 729.

To refine our estimate, we would square this number (27.37 x 27.37) to get 749.24, which is higher than 729. We would then adjust our estimate downwards and repeat the process until we get as close to 729 as possible.

By demonstrating this process to the class, they would learn how to use the averaging method to find the square root of 729 and gain a better understanding of how square roots work.

Step 1: Find the first order estimation

- Ask students to find the average of the first two digits of the number, 7 and 2.
- (7 + 2) / 2 = 4.5

- This gives us our first order estimation of the square root of 729, which is 4.5.

Step 2: Adjust the estimation

- Show students that 4.5 squared is 20.25, which is less than the original number.
- Explain that the square root should be slightly larger than 4.5.
- Ask students to add 0.5 to the first estimation, giving us 4.5 + 0.5 = 5.

Step 3: Calculate the average

- Find the average of the previous estimation (5) and the first two digits of the number (7 and 2):
- (5 + 7 + 2) / 3 = 4.666...

- Round this average to two decimal places, giving us 4.67.

Step 4: Repeat the process

- Repeat steps 2 and 3 until you reach the desired level of accuracy.
- In this case, 4.67 squared is 21.8769, which is very close to 729.

Final Answer:

- Therefore, the square root of 729 using the averaging method is approximately 4.67.

Note:

- Emphasize to students that the averaging method is not exact, but it provides a reasonable estimation.
- Encourage them to use a calculator for more precise results.