How do you work out the square root of a number?

Question

I am not that good at maths and cant remember how to work out the square root .How do you do it !

Answer 1

6 x 6 = 36
6 is the square root of 36.
You can always use a calculator w/ a square root function, too.

Answer 2

Here's a method that doesn't get as tedious as quickly as Newton's method, and avoids the problem having to round repeating decimals somewhere. Let's try a number that looks really formidable:
√586756
First, pair off the digits, starting at the right:
√58 67 56
Find the largest square less than the first digit or pair. Enter its square root above and the number below:
. . 7
√58 67 56
. 49
Subtract, bringing down the next pair:
. . 7
√58 67 56
. 49
. 11 67
Multiply the answer you have so far by 20 and use this for a divisor to get the 2nd digit:
. . . . . 7 . 6
. . . √58 67 56
. . . . 49
140|11 67
Now, the trick that makes the method work. Replace the 0 in the divisor with the new digit, and multiply by that digit:
. . . . . 7 . 6
. . . √58 67 56
. . . . 49
. 146|9 67
. . . . 6|8 76
Subtract again, bring down the next pair.
. . . . . 7 . 6
. . . √58 67 56
. . . . 49
. 146|9 67
. . . . 6|8 76
. . . . . . . 91 56
Make a new divisor by multiplying by 20 again OR simply add the old "divisor" and new digit:
. . . . . 7 . 6
. . . √58 67 56
. . . . 49
. 146|9 67
. . . . 6|8 76
. . 1520|91 56
Multiply out as before:
. . . . . 7 . 6 . 6
. . . √58 67 56
. . . . 49
. 146|9 67
. . . . 6|8 76
. . 1526|91 56
. . . . . . 6|91 56

Because I selected an exact square for the demonstration, everything came out even. If you start with a number that isn't a perfect square, you can continue the process until you reach the desired accuracy.

Answer 3

From "Ask Dr. Math:"

The square root of a number is just the number which when multiplied by itself gives the first number. So 2 is the square root of 4 because 2 * 2 = 4.

Start with the number you want to find the square root of. Let's use 12. There are three steps:


Guess
Divide
Average.
... and then just keep repeating steps 2 and 3.

First, start by guessing a square root value. It helps if your guess is a good one but it will work even if it is a terrible guess. We will guess that 2 is the square root of 12.

In step two, we divide 12 by our guess of 2 and we get 6.

In step three, we average 6 and 2: (6+2)/2 = 4

Now we repeat step two with the new guess of 4. So 12/4 = 3

Now average 4 and 3: (4+3)/2 = 3.5

Repeat step two: 12/3.5 = 3.43

Average: (3.5 + 3.43)/2 = 3.465

We could keep going forever, getting a better and better approximation but let's stop here to see how we are doing.

3.465 * 3.465 = 12.006225

That is quite close to 12, so we are doing pretty well.

Answer 4

ok the square root of a number is the number that can be multiplied by the same number to give you the number inside the root... example 2*2=4
this means the square root of 4 is 2 because you can multiply 2 by the same number which is 2 and the result is 4... for numbers that dont have a perfect square root you must find a number that has a perfect square root and multiply it by another number... example the square root of 8. 8= 4*2 the square root of 4 is 2 which means the result will be the number with the perfect root outside of the root and the number with no exact root inside the root. so it will look like this.... 2square root of 2

Answer 5

to find the spuare root of any # U just find a # that will give U the # that is inside the square root sign when multiplied by that same #
example: 2 multiplied by 2 is 4, then the square root of 4 is 2.

p.s good luck

Answer 6

if it's a perfect square, memorization or a calculator would be fine. if it's not a perfect square and you can't just give the calculator's decimal answer, you do a factoring tree.
ex: square root of 48=16 * 3. 16 is a perfect square, so you can take that outside the radical, so it will be 4 times the square root of 3.

Answer 7

You have to work out the square root of something with trial and error (unless you have a calculator, then just press the √ and then enter the number!)
The square root if you are going to be forced to work it out mentaly is the opposite of squring a number e.g the square root of 36 is 6, 6x6 (or to the power of 2) is 36.

Answer 8

http://www.mathsisfun.com/square-root.html
Hope this address is of any help


square root of 64 is 8 because 8 times 8 is 64
16 is 4 4 times4 is 16 and so on.

Answer 9

Definition: The square root of a number n, is a number r, such that r*r or r^2 equals x.

Example: sqrt4=2, bcoz 2*2=4.
sqrt9=3, bcoz 3*3=9.

Answer 10

you can use newtons method to approximate the square root of a function.
if you want to do it by hand.

or use a calculator.