how do you figger out a square root of someting?

Question

I,e, a square root of a hundred is? and how do you work that out, on any number.

Answer 1

You just think about a number times itself. It's like what times what is 100. 10*10 =100 so the sqrt100=10

Answer 2

Well you can use a square root button on a calculator or if you know the square numbers 1, 4, 9, 16, 25................ that is the number which you get when you square a number eg 1 x 1 = 1
2 x 2 =4, 3 x 3 = 9 etc etc 10 x 10 = 100 then as many answeres have already said you can find the square root (although it could be 10 or -10.)
I have a book (Red Hot Math Starters by Katheryn Stahl) which gives a method called Asian Square roots where you start subtracting the odd numbers in order eg square root of 16
16 - 1 = 15
15 - 3 = 12
12 - 5 = 7
7 - 7 = 0
having reached 0 you count how many subtractions you have done 4 so square root of 16 is 4
however this still doesn't help if you are not working with a non square number

Answer 3

For "small" perfect squares, you need to know the multiplication table, and notice when a number is equal to some number times itself.
For large perfect squares, you can factor into primes. Each exponent must be even for a perfect square, so to find the square root, cut each exponent in half. For example, 7056 = 2^4*3^2*7^2, so sqrt(7056) = 2^2*3*7 = 84.
For non-perfect squares, how you leave your answer depends on the problem. Sometimes, you take the square root of the square factors, and leave the rest under the square root sign, like sqrt(18) = sqrt(9*2) = sqrt(9)*sqrt(2) = 3sqrt(2).
Other times, using a calculator and rounding if necessary, is OK. There is a way to figure this out "by hand" - the square root algolrithm - but it's easier with a calculator.

Answer 4

Raccoon's link provides no fewer than three separate methods of finding square roots. These include:

Cut and try, in which you make successively better guesses at the answer, square the result, and find out whether it is too high or too low. In its machine-implemented form, this is known as the binary search, in which you reduce the range of possibilities by half in each step. This procedure has broad applicability. This is the best strategy to use when guessing a number, for example, where you are only given the information whether the guess is too high, too low, or exact.

This is somewhat speeded up in the procedure described in the link by biasing the next guess somewhat by determining whether the result is way off or just a little bit off.

Another procedure, not described in the article itself but in the comments afterward, is called the Babylonian method. This is also called Newton's method because this procedure can also be thought of as using the derivative of the square root function to find the next guess, a procedure Newton (presumably) came up with first.

Unlike the binary search, the Babylonian method is specific to finding square roots, requires a division plus some other simple arithmetic rather than a multiplication to find the next guess, but just about doubles the number of significant figures in the accuracy of the guess for every guess-divide cycle. This makes it a good method to use if you already have a fairly good estimate for the square root that you want to refine.

The third method, resembling long division on steroids, is called the algorithm approach. This is a misnomer because the binary search and the Babylonian method are also algorithms. The algorithm approach was the (first) method I was taught in school for finding square roots. As is mentioned in the comments at the end, this is a good method for extracting roots by computer because the computer can do the necessary operations faster than with long division, but I have trouble remembering the procedure and now prefer the Babylonian method because it is easier for me to understand and remember.

Answer 5

HERE IS A GENERAL PROCEDURE FROM 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 6

i dont think you can work it out that way without a calculator,
the only thing you can do for example you can say 9 squared is 81 so you know it is more than that, 11 squared is 121 so you know it is less than that so the answer for 100 is 10

it would be a lot more difficult to work it out for example if you wanted to find the square root of a number like 73

you would have to say it was somewhere between 8 and 9 then you would get into parts of numbers, and i dont know about you but my maths wouldnt be good enough without using a calculator

i am going to come back to this question tomorrow because i would be interested if their is a simple solution other than using a calculator

best wishes


vici xxx

Answer 7

sqrt(x) = x^(1/2)

You can use a calculator to evaluate the square root, or take the number under the root sign and raise it to the power of 1/2.

For your example, you know that the square root of 100 is 10 because 10*10 = 10^2 = 100

Answer 8

√100 = 10
10 x 10 = 100

√25 = 5
5 x 5 = 25

√16 = 4
4 x 4 = 16

Hope these examples help.

Answer 9

a square root is the opposite of a square.

so to understand a square root, you must first know what a square is.

a square is when you multiply any number by itself.

so going along with your question of how to find the square root of 100, you must first know what number multiplied by itself gives you 100.

10 times 10 is 100.

therefore, the square root of 100 is ... 10.

furthermore, 9 times 9 is 81

that makes the square root of 81 to be 9

etc.

hope this helped.

Answer 10

its 10

10 squared is 100 so the square root of 100 is 10

ie. 5x5 = 25 square root of 25 = 5