calculate square roots without a calculator?

Question

ppl how do u calculate a square root without a calculator
its 4 a test
ex. 20
answer asap

Answer 1

If you can remember your perfect squares then it's no problem. 8 squared is 64 and 9 squared is 81, therefore the square root of 69 must be between 8 and 9. Hope my advice helped.

Answer 2

of course it is possible to calculate square roots without a calculator, But nobody does this anymore, except for the easy ones where the numbers themselves are squares; these would be 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144. The square roots of these numbers are 2, 3, 4, 5, 6, 7,8, 9, 10, 11, 12 in order.

Now if you were looking for the square root of say 12, it would be somewhere between 3 and 4, because the square of 3 is 9 and the square of 4 is 16, and 12 is obviously between them. Likewise the square root of twenty is somewhere between 4 and 5 for the same reason.

If you need to know more about calculating square roots, your teacher would surely have covered it in class because it isn't exactly easy to do, and like I said, since calculatorscame along nobody does it by hand anymore.

Good luck!

Answer 3

Yes, it can be done. One way is by iterations. Square-root of a number can be considered as the repeated factor, i.e. find two factors of the number that is equal.
So, you may start from any number between 1 and 20, say 4, which is a good choice. So you have 4 and 5, where the root is somewhere in between. Without calculator, you can consider finding their arithematic average, i.e. (4+5)/2=4.5=9/2, and find 20/(4.5), and you have the two factors 9/2 and 40/9 = 4.4444..., then try 20/((9/2+40/9)/2) = 20/((81+80)/36) = 720/161 = 4.472 (3 dec pls), where sqrt(20) = 4.4721359549995793928183473374626

Since without calculator, may leave your answer in fraction form.

However, in a test without calculator, and your workings reach a situation where by you need to find such a value, first check the following:
a. Have you made a mistake somewhere that led you to this unexpected state? Check working.
b. Could it be a typo error in the question? Ask, or wait for someone to ask.
c. Leave the answer as sqrt(20), or slightly better, 2 x sqrt(5)

Answer 4

can someone help me do step by step in finding the square root to 3 decimal places for number 2404 without a calculator

Answer 5

you can't square root 20 (or at least i cant withou a calculator). only 4, 9, 16, 25, 36, 49, 64, 81, 100, etc.

Answer 6

there are ways to do this, but i'm surprised if a teacher would ask you to calculate the square root of 20 on a test unless you were in college or an upperclassman in high school, and it doesn't seem like you are.

Answer 7

break 20 in to factors like 5*4 then take 4 out and u r left with 2underroot5. i use this method. i think ur teacher wont mind underoot of 5. then i have to use calculator secretly

Answer 8

This link will be helpful to you: http://www.homeschoolmath.net/teaching/square-root-algorithm.php

Answer 9

i think you would have to guess and check
an it somthi ng beween 4.4 and 4.5