how to get the square root of a number without using calculator?

Answer 1

sqrt(x) = sqrt(n*n)
sqrt(x) = n

which means you can get the square root of that number (x) if there is a number (n) that when you multiply by itself the answer is the same as that number (x).

Answer 2

Well you have to remember the perfect squares of couse 1,4,9,16,25,36,49,64... however when you're finding the square root of a number like 44 you have to simplify it 11 times 4 {these numbers are still inside the square root}. Now you the square root of 4 is 2 but you can't simplify 11 anymore so that is still inside the radical (radical just means square root just ascientific way of saying it) sign. The answer will read 2 times the square root of 11. If you don't believe me then try out the square root of 36 simplify 9 times 4. Square root of 9 is 3 and lets keep that 4 in the radical sign. So 3 times the square root of 4 is 6.

Answer 3

The grade school algorithm is to take integers in the number you have and mark them of by twos starting at the decimal point. EX: sqrt 72345 ,mark off the 45, then 23 and leave the 7 by itself. Then you ask what number squared is the largest in 7, in this case "2". square 2 and subtract from 7and "bring down" the next pair to get 323. The next divisor is double the two to get 4 and ask what the largest number in the 40's which divides into 323, in this case 46. . Multiply 46 by "6" and subtract from 323 to get 47, drop down the next pair of numbers to get 4745. You now have that the sqrt starts with a 26. Double the 26 to get 52 and ask what number in the 520,s is the largest that will divide 4745. About 529. Multiply 529 by "9" and find it is larger than 4745 so use 528 times "8" subtracted from 4745 yields 521. The sqrt of 72345 is close to 268. The next pair dropping down would be 00 , coming from after the decimal point, and the new number to consider is 52100 and the divisor is in the 2(2680)'s...namely 5369 which means the answer is closer to 268.9. the "true"answer is 268.970 through 3 decimals. Try this procedure on some sqrts.

Answer 4

Do long division by using ONLY prime factors. They are:
2,3,5,7,11,13,17, 19, 23, etc
keep on dividing with one prime factor, until is is not possible any more, and then try the next one.

e.g Find the square root of 8100
First divide by 2 - this is possible 2 times
Then divide by 3 - this is possible 4 times
Then divide by 5 - this is possible 2 times
so, yoy have now: 2² x 3 to the power 4 x 5 ²
Divide each index by 2
It gives you; 2 x 3 power 2 x 5 = 90
So the square root of 8100 = 90

Answer 5

the way you figure out a square root of a number is to break it down to all prime factors. then for every pair you take one and multiply them
example
81=3x3x3x3
so for every group of 2 i take 1 so
3x3=9
9 is the square root of 81

another example if the number is not a perfect square
18=2x3x3
square root of 18 = 3x (that square root of 2)

Answer 6

A simple way to get the square root of N using the Babylonian method (or Newton's method) is:
start with x=1 then find a new x according to:
new x=1/2*(x+n/x)
Repeat and it will get closer and closer to the square root.

Answer 7

http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Digit_by_digit_calculation

The digit by digit long division method was taught when I was in school. It is explained in the reference above. It gives an exact answer for as long as you want to carry out the steps. Other methods can be used to approximate the answer.

Of course there is always the log table...a log divided by 2 will give you log of the square root (log of 81 = 1.908485; divide by 2 to get 0.95424; take the antilog and get 9.0000). The hard part may be locating a 5 place log table.

Answer 8

if you can calculate a number raised to 1/2 without a calculator then this can be your solution.

n^1/2 = SQR/n so for example SQR/4 = 4^1/2

Answer 9

you use Calculus. If you must ask, you are not at the level to do it yet. it has to do with limits, taylor series and so on. if you just want to know for fun, you can guess by looking at it and come close. roots are just like powers.

example
2^2=4 sqroot(4)=2

3^2=9 sqroot(9)=3

so if you have
sqroot(5) you know it is more than 2, but less that 3

Answer 10

You have a lot to choose from,
http://en.wikipedia.org/wiki/Methods_of_computing_square_roots