Posted by **sapna** on Tuesday, December 18, 2012 at 8:05am.

how to find the square root of 404.41 with steps please help

- maths --plse help me.. -
**Reiny**, Tuesday, December 18, 2012 at 8:31am
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.

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