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# Is it possible to find the square root of an number without a calculator.

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Is it possible to find the square root of an number without a calculator.

Guest Oct 17, 2014

#2
+81007
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There are probably many methods........you can read about a couple of them here......http://mathforum.org/dr.math/faq/faq.sqrt.by.hand.html

(Be sure to scroll to the bottom of the page for some links to others.....)

CPhill  Oct 17, 2014
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#1
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i dont know i belive it would be very hard to do that though it would take a math wiz

thelonewolf  Oct 17, 2014
#2
+81007
+8

There are probably many methods........you can read about a couple of them here......http://mathforum.org/dr.math/faq/faq.sqrt.by.hand.html

(Be sure to scroll to the bottom of the page for some links to others.....)

CPhill  Oct 17, 2014
#3
+5

Yes, one approach is to use a divide and average approach.

Example: $$\sqrt{3}$$

Guess an approximate answer, say 2.

• Divide to obtain 3/2 = 1.5 and average to obtain (2 + 1.5)/2 = 1.75.
• Divide to obtain 3/1.75 = 1.71428 and average to obtain (1.75 +  1.71428)/2 = 1.73214
• Divide to obtain 3/1.73214 = 1.73196 and average to obtain (1.73214 + 1.73196)/2 = 1.73205

This is already close to the value provided by a calculator and becomes even more accurate if you use more decimal places and repeat the divide and average a few more times.  This method was known for thousands of years.

Guest Oct 17, 2014
#4
+17711
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Before the creation of hand-held calculators, an algorithm was taught in algebra classes; it can be found at

http://www.basic-mathematics.com/square-root-algorithm.html

geno3141  Oct 17, 2014
#5
+81007
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Notice that the "divide and average" method is very simple.......the only problem with the method - and some others, as well - is that the numbers generated are difficult to work with........unless you have a calculator......!!!!

CPhill  Oct 17, 2014

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