There are methods based on numerical approximations. Look up Newton Raphson method for one that is relatively easy to use.
Alternatively:
Here is an almost-forgotten art: one that, with the advent of electronic calculators, will likely survive to the twenty-first century only on paper and in the memories of oldsters.
What is the number you want to find the square root of? Here's one we'll use: <b>46656 </b>
First, divide the number to be square-rooted into pairs of digits, starting at the decimal point. That is, no digit pair should straddle a decimal point. (For example, split 1225 into "12 25" rather than "1 22 5"; 6.5536 into "6. 55 36" rather than"6.5 53 6".)
Then you can put some lines over each digit pair, and a bar to the left, somewhat as in long division. <b> +--- ---- ---- | 4 66 56 </b>
Find the largest number whose square is less than or equal to the leading digit pair. In this case, the leading digit pair is 4; the largest number whose square is less than or equal to 4 is 2.
Put that number on the left side, and above the first digit pair. <b> 2 +--- ---- ---- 2 | 4 66 56 </b>
Now square that number, and subtract from the leading digit pair. <b> 2 +--- ---- ---- 2 | 4 66 56 |-4 +---- 0 </b>
Extend the left bracket; multiply the last (and only) digit of the left-hand number by 2, put it to the left of the difference you just calculated, and leave an empty decimal place next to it. <b> 2 +--- ---- ---- 2 | 4 66 56 |-4 +---- 4_ | 0 </b>
Then bring down the next digit pair and put it to the right of the difference. <b> 2 +--- ---- ---- 2 | 4 66 56 |-4 +---- 4_ | 0 66 </b>
Find the largest number to put in this blank decimal place such that that number, times the number already there plus the decimal place, will be less than the current difference. For example, see if 1 * 41 is ≤ 66, then 2*42 ≤ 66, etc. In this case it's a 1. Put this number in the blank you left, and in the next decimal place on the result row on the top. <b> 2 1 +--- ---- ---- 2 | 4 66 56 |-4 +---- 41 | 0 66 </b>
Now subtract the product you just found. <b> 2 1 +--- ---- ---- 2 | 4 66 56 |-4 +---- 41 | 0 66 |- 41 +-------- 25 </b>
Now, repeat as before: Take the number in the left column (here, 41) and double its last digit (giving you 42). Copy this below in the left column, and leave a blank space next to it. (Double the last digit with carry: for example, if you had not 41 but 49, which is 40+9, you should copy down 40+18 which is 58.) Also, bring down the next digit pair on the right. <b> 2 1 +--- ---- ---- 2 | 4 66 56 |-4 +---- 41 | 0 66 |- 41 +-------- 42_ 25 56 </b>
Now, find the largest digit (call it #) such that 42# * # ≤ 2556. Here, it turns out that 426 * 6 = 2556 exactly. <b> 2 1 6 +--- ---- ---- 2 | 4 66 56 |-4 +---- 41 | 0 66 |- 41 +-------- 426 | 25 56 |- 25 56 +------------- 0 </b>
When the difference is zero, you have an exact square root and you're done. Otherwise, you can keep finding more decimal places for as long as you want.
Here is another example, with less annotation. <b> 7 . 2 8 0 1 ... +---------------------- 7 | 53 . 00 00 00 00 00 | 49 +---------------------- 142 | 4 00 | 2 84 +---------------------- 1448 | 1 16 00 | 1 15 84 +---------------------- 14560 | 16 00 | 0 +---------------------- 145601 | 16 00 00 | 14 56 01 +---------------------- | 1 43 99 00 ... </b>
To find the square root of a number you multiply that number by it self twice.(example) the square root of 9 ? the square root of nine is 81 as 9X9=81. square root of 4 ? th square root of is 16 as 4X4=16.
There is no square root for a negative number. It is an imaginary number.
Cube root.
What I do is find the square root of that number and then find the square root of the answer. Example: 1,296. Square root of 1,296, which can be done easily on most calculators: 36 Square root of 36: 6 Your answer is 6 If you want to check up on that, go ahead, but 6x6x6x6=1,296
Type in the number that you want to square root, then hit the √ button.
To find the square root of a number you multiply that number by it self twice.(example) the square root of 9 ? the square root of nine is 81 as 9X9=81. square root of 4 ? th square root of is 16 as 4X4=16.
square root it
to find the square root of a number you need to find the number that multiplied by its self is that number example: the square root on 9 is 3 it is 3 because 3 x 3 - 9
Press the square root button on your calculator.
There is no square root for a negative number. It is an imaginary number.
To find the square root of a number you must find the number that can multiplied by itself to equal that number Ex: the square root of 9 is 3 because 3*3=9
It is no tpossible to find the square root of an unknown number. You can, however, represent it as x0.5 or √x so that the value of the square root can be evaluated when the value of x is known.
Use a calculator (if you need) to find the principal square root. The second square root is the negative of the number.
We will walk through the definition of the square root of 63, find out whether the square root of 63 is rational or irrational, and see how to find the square root of 63 by the long division method. ... Square Root of 63.
You can't find the square root of -10 because you can't find the square root of any negative number. But we have something to represent the answer, i, i is a imaginary number.
An irrational number is a number that never ends. An example of an irrational square root would be the square root of 11.
Cube root.