write two consecutive perfect square closest to 20. estimate the value of square 20 . square your estimate. use this value to revise your estimate. keep revising your estimating until the square of the estimate is within 1 decimal place of 20.
my eng is limited, can anyone help me the last sentence mean? " keep revising your estimating until the square of the estimate is within 1 decimal place of 20. ""
Thank you!
4^2 = 16
5^2 = 25
so, 4.5 is a good first guess.
4.5^2 = 20.25
too big
4.4^2 = 19.36
4.45^2 = 19.80
4.46^2 = 19.89
4.47^2 = 19.98
4.48^2 = 20.07
So, you want something between 4.47 and 4.48
keep going.
The sentence "Keep revising your estimate until the square of the estimate is within 1 decimal place of 20" means that you should continue adjusting your estimate until the square of the estimate is very close to 20, only differing by one digit after the decimal point.
Let's break it down step by step to solve the problem:
1. Find two consecutive perfect squares closest to 20:
Start by finding the square root of 20. It is between 4 and 5 (since 4 squared is 16 and 5 squared is 25). The two consecutive perfect squares closest to 20 are 16 (4 squared) and 25 (5 squared).
2. Estimate the value of the square root of 20:
Since the square root of 20 is between 4 and 5, we can estimate it as 4.5 (the average of 4 and 5).
3. Square your estimate:
Square 4.5: (4.5)² = 20.25
4. Revise your estimate:
Since 20.25 is slightly larger than 20, we need to revise our estimate. We can try a smaller value this time.
5. Revised estimate:
Let's try 4.4 as our revised estimate.
6. Square the revised estimate:
Square 4.4: (4.4)² = 19.36
7. Evaluate the result:
The square of the revised estimate, 19.36, is still smaller than 20. We need to revise our estimate again to get a closer value to 20.
8. Keep revising your estimate:
Repeat steps 4 to 7 until the squared estimate is within 1 decimal place of 20. Continue adjusting the estimated value by small increments and squaring it, until you arrive at a value that is very close to 20 when squared.
Keep repeating steps 4 to 7 with revised estimates until the square of the estimate is within 1 decimal place of 20.