SOLUTION: I have to solve an square root without a calculator. It has to be in a(square root symbol) b. Help please!

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Question 1209551: I have to solve an square root without a calculator. It has to be in a(square root symbol) b. Help please!
Found 4 solutions by math_tutor2020, Edwin McCravy, mccravyedwin, ikleyn:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Your question seems a bit vague, but I'll try my best to answer.
It sounds like you're given something like sqrt%2896%29 and your teacher wants it simplified into the form a%2Asqrt%28b%29 where a,b are integers and b > 0.

I'll provide two examples.

------------------------------------------------

Example 1
sqrt%2872%29+=+sqrt%2836%2A2%29 See note below

sqrt%2872%29+=+sqrt%2836%29%2Asqrt%282%29 Use the rule sqrt(x*y) = sqrt(x)*sqrt(y) where x,y cannot be negative.

sqrt%2872%29+=+sqrt%286%5E2%29%2Asqrt%282%29

sqrt%2872%29+=+6%2Asqrt%282%29 Use the rule sqrt(x^2) = x where x is nonnegative.

Note: I factored 72 so that one of the factors is a perfect square.
We want this factor to be the largest perfect square possible.

------------------------------------------------

Example 2
sqrt%28245%29+=+sqrt%2849%2A5%29

sqrt%28245%29+=+sqrt%2849%29%2Asqrt%285%29

sqrt%28245%29+=+sqrt%287%5E2%29%2Asqrt%285%29

sqrt%28245%29+=+7%2Asqrt%285%29

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Here is how I was taught to take the square root of a number back in about 6th
grade before anybody had heard of an electronic computer or calculator.  It
reminds one of the algorithm of long division, but it's lots more complicated. 
See if you can figure out how we took the square root of 2 back in 1940-1950. 

            1.  4   1   4   2
           √2. 00  00  00  00      <--you can keep adding pairs " 00 " 
            1
        20| 1  00
        24|    96
        280|    4  00
        281|  281
        2820| 119  00
        2824| 112  96
        28280|  6  04  00
        28284|  5  75  68  
                   28  32


Edwin

Answer by mccravyedwin(407) About Me  (Show Source):
You can put this solution on YOUR website!

Here's the square root of a perfect square by the "ancient" method.

            2   9   4
           √8  64  36
            4
         40|4  64
         49|4  41
           580|23  36
           584|23  36
                    0 
√(86436) = 294


Edwin

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
I have to highlight%28cross%28solve%29%29 compute highlight%28cross%28an%29%29 a square root without a calculator.
It has to be in a(square root symbol) = b. Help please!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


I asked Google with these keywords "algorithm of finding square root of an integer number manually".

Google knows everything, the major thing is to ask a right question.


This time Google provided these links:

(a) wording description by Artificial Intelligence

https://www.google.com/search?q=algorithm+of+finding+square+root+of+an+integer+number+manually&rlz=1C1CHBF_enUS1071US1071&oq=algorithm+of+finding+square+root+of+an+integer+number+manually&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCjM3MjY3ajBqMTWoAgiwAgE&sourceid=chrome&ie=UTF-8


(b) Video-lessons

https://www.youtube.com/watch?v=HBdVVFqTrUU

https://www.youtube.com/watch?v=x4D5bPqONAE


It is how my teachers taught me many years ago, in my 6-th grade.



To be honest, after learning this algorithm in school, I did not use it in my life NO ONE single time.
(Although all my life was making scientific computing).

So, in my view, this knowledge does belong to the category of absolutely useless subjects.