How do you find square roots which are no perfect?

Question

like what the hell is the squareroot of 31? How do you find out?

Answer 1

Example root 30???
Guess any approximation: 5
30 / 5 = 6
Average of 5 and 6 is 5.5.
30 /5.5 = 5,45454545454545
Average of 5.5 and 5,454 is 5.48
30 / 5.48 = 5.4771
Average of 5.48 and 5.4771 is ... .
...

Th

Answer 2

The simple fact is that you don't. That's what calculators are for. Punch in a calculator sqrt(31) and that's it.

However, in later math, you don't use approximate values anyway, and you leave your answer as sqrt(31). You'll also eventually learn that square roots multiply together, so if you had something like sqrt(31) and you wanted to multiply sqrt(7), all you'd have to do is multiply the insides to get sqrt(217).

It's the properties of square roots that are more important, instead of the actual calculation. If you needed the approximate number, that's what the calculator is for.

Answer 3

x.....x^2

0.....0
1.....1
2.....4
3.....9
4....16

etc.

Then, the square root is this:

x.......sqrt x

0.........0
1.........1
4.........2
9.........3
16.......4

How do you find the square root of a number if it is not a perfect square? There are many methods. You already got lots of answers.

But one easy and quite fast method is this one:

If sqrt 9 = 2 and sqrt 16 = 4, then you can more or less guess what the sqrt 10 could be, perhaps 3.1

So, just pic a calculator and multiply until you get a number that is as close as you want it to be from 10.

If you consider that

3.1 x 3.1 = 9.61
3.2 x 3.2 = 12.24

then sqrt 10 will be a number from the interval (3.1,3.2). Try with 3.15, etc., until you get as decimal digits as desired

Ana



Ana

Answer 4

I cant' remember exactly but i remmeber an alorithm..... YOu keep getting approximations that converge to the right answer, but you'd still need to use a calculator to do it accuratly.

Like the other user said....you make an educated guess... then square it. Depending on how accurate you want..you change the value of the decimal.

Answer 5

without a calculator it can be done by this :
5x5=25 (we know this )
6x6=36 (we know this)
Now by knowing that , the square root must be 5. x (x unknown )
there is an 11 digit difference between 25 and 36,
so it would be slightly above the middle=5.57 (rounding to nearest hundredths

Answer 6

There's a good description of the algorithm at

http://jwilson.coe.uga.edu/EMT668/EMAT4680.folders/Rice/sq%20root%20alg%20stuff/sq%20root%20alg.html

and another explaination at

http://jwilson.coe.uga.edu/EMT668/EMAT4680.folders/Nowlen/squareroot.html

And yes, before you ask, there are algorithms for cube root, etc. And they're a pain in the αss ☺ Find a calculator or a log table.


Doug

Answer 7

There is a method just similar to division. May be difficult to explain/demonstrate here.

Answer 8

Myself, I use a calculator, but I've long finished taking exams.