how to find the square root of 404.41 with steps please help
It was not good I can't understand it
To find the square root of 404.41, you can follow these steps:
1. Start by estimating the value of the square root. You can do this by finding the nearest perfect square below 404.41. In this case, the nearest perfect square is 400 (20 x 20), and the square root of 400 is 20. So, 20 is a reasonable estimate for the square root of 404.41.
2. Next, set up the square root equation using the estimated value:
√404.41 = 20 + x
3. Now, square the estimated value and subtract it from 404.41 to get the remainder:
404.41 - 400 = 4.41
4. Bring down the next two decimal places from the original number (404.41) to the remainder (4.41):
Add a decimal point in the quotient, above the decimal point in the original number:
√404.41 = 20.0 + x
5. Double the current quotient (20.0), and write it as the next digit in the quotient (x):
√404.41 = 20.0x + x
6. Multiply the current divisor (x) by the current quotient (x), and write the result under the remainder (4.41):
Multiply x by x: x * x = x^2
7. Subtract the result (x^2) from the remainder (4.41):
4.41 - x^2 = 4.41 - x^2
8. Bring down the next two decimal places from the original number (404.41) to the remainder (4.41):
Add two zeros after the decimal point in the quotient, and add a decimal point in the new number:
√404.41 = 20.0x + x + 0.00
9. Double the current divisor (20.0x), and write it as the next digit in the quotient (x):
√404.41 = 20.0xx + x
10. Multiply the current divisor (20.0x) by the current quotient (x), and write the result under the remainder (4.41):
Multiply 20.0x by x: 20.0x * x = 20.0x^2
11. Subtract the result (20.0x^2) from the remainder (4.41):
4.41 - 20.0x^2 = 4.41 - 20.0x^2
12. Repeat steps 6 to 11 until you reach the desired level of precision or until the remainder becomes zero.
By following these steps, you can approximate the square root of 404.41.
How to solve decimal square root
No use
go to...
Are you suggesting a "pencil-and-paper" method?
I will show you three ways.
1.
This is what I taught years ago, before we had calculators
http://www.homeschoolmath.net/teaching/square-root-algorithm.php
look at the method labeled "algorithm"
2.
You could also use Newton's Method
-start with a reasonable guess
I guess 20
-divide 404.41 by 20 to get 20.22505
average that answer with my guess
(20 + 20.22505)/2 = 20.11025 ---> new guess
make that your new guess and repeat:
404.41÷20.11025 = 20.109645..
(20.109645+20.11025)/2 = 20.10994779 --> new guess
404.41/20.10994779 = 20.10994778
(20.10994779+20.10994778)/2 = 20.10994779 --> the same as before
so √404.41 = 20.10994799 correct to 8 decimal places in 3 steps
If you start with a silly guess, like 10 , eventually you will get the answer, it will just take longer.
3.
of course you could also just do :
√404.41 = 20.10994779 on your calculator.