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Calculating Square Roots


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In the cartoon thread the gag was “what’s the square root of 5,248?” These days we just plug the number into the calculator and push the button. 
 

For the life of me, I can’t remember how we figured that out before we had calculators? I vaguely remember a laborious process of guesstimating. 
 

Any of you math wizards recall how?

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Guess.

Divide by the Guess, add the guess, and divide by two. This gives you a new guess.

 

Example

25. We will guess the square root is 4

25 / 4 = 6.25, plus four equals 10.25 / 2 = 5.125. 5.125 is the new guess

 

25 / 5.125 equals 4.87, plus 5.125 equals 10.003, divided by 2 equals 5.0015.

 

New guess is five

 

25 / 5 = 5 + 5 = 10 / 2 = 5

 

Answer is five

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I just experimented, and cube Roots works the same way. Just has one more step.

 

27. We will guess that the cube root of 27 is 2

 

27 / 2 / 2 =6.75 (because this is a cube root we have to do things three times, so we divide by the Guess twice, add the guess twice, and then divide by 3)

 

6.75 + 2 + 2 = 10.75, / 3 equals 3.5888

 

New guess 3.58

 

27 / 3.58 / 3.58 =2.106 plus 3.58 3.58 =9.266 divided by 3 equals 3.088

 

new guess 3.1

 

27 / 3.1 / 3.1 =2.809 + 3.1 + 3.1 =9.009 / 3 = 3.003

 

New guess is three

 

27 / 3 / 3 = 3 + 3 + 3 = 9 / 3 = 3

 

Cube root of 27 is 3

 

 

Edited by Alpo
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17 minutes ago, Abilene Slim SASS 81783 said:

That headache I got somewhere around 1965-1966 is coming back…

Then stop reading this post right now.

 

For square root of a number, take the log of the number, divide the log by 2, and take the antilog of the result.

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12 hours ago, John Kloehr said:

Then stop reading this post right now.

 

For square root of a number, take the log of the number, divide the log by 2, and take the antilog of the result.

 

On your scientific calculator,

 

Enter the number you want to find the square root of.

Press the Log button

Divide the answer by 2

Press the 10x button. On the calculator the x is to the top right of the number 10. Forum doesn't allow me to type superscripts.

 

Square root of 5,248

log = 3.720

Divide by 2 = 1.86

10x = 72.444

 

Square root of 5248 = 72.444

72.444 X 72.444 = 5248.133

 

If you don't round any of the numbers the answer is 72.443081105099333012590465335873

 

 

Edited by Sedalia Dave
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Or ever had to worry about a dangling participal. (sp)

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21 hours ago, Alpo said:

Is that anything like 420?

That's next month....   SB

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On 3/19/2024 at 3:58 PM, Sgt. C.J. Sabre, SASS #46770 said:

RIGHT. And even after writing a book, I've STILL never needed to diagram a sentence.

Having myself just put significant effort into putting this sentence together, I have no desire to take it apart.

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when i was i college we were forced to switch from the slide rule to calculators , i selected the HP35 others went with the texas instruments , both had their favorable recommendations as well as their drawbacks , , neither were perfect and both had different operating systems , but i could still use my slide rule just not as fast as those that perfected their calculators [i guess my first resistance to the progress] now-a-days all the calcs for trigonometry , geometry , algebra and integrals can be done on a computer  as well as a lot more if your math extrends beyond what some of us were exposed to in college , 

 

i can still do long division - old school as well as most other things if given enough time ......on paper with the full written dribble we always had to do to prove our work , but i fear none of our kids are being taught those things anymore , my algebra teacher emphasized ballistic calculations back in high school - he thought , no he knew , we would need them in VN , but today im thinking no teacher of math even understand that , or why it might be needed , 

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My wife was reading an 1890 census records in her genealogy application.
She remarked how none of the kids today can read these... in script.

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