what is the formula to find out square roots?

Question

is there one or is it a guessing game till you find out

is there a way to find a sqaure root with out guessing

Answer 1

There's no formula for square roots.

Answer 2

It's not hard to memorize basic squares; 2 squared = 4, 3 squared = 9, 4 squared = 16. Otherwise, you can use a calculator, the square root symbol is √.

If you're trying to find the square root of a number that isn't a perfect square, you can estimate the value by comparing how close it is to a perfect square. For example, the square root of 25 is 5, therefore, you can assume that the square root of 24 is a little less than 5.

The square root itself is a function, therefore, there aren't specific mathematical steps to go through to determine the value without a calculator; the square root is the step. The only ways to determine square root are just knowing, calculator and estimating.

Answer 3

The best way to find the square root is to use a calculator, but
I assume this is not allowed. So, you begin with a guess.
Say you want to find the square root of 24.
This means what number can be multiplied by itself to give 24?
Try 5: 5x5 = 25. This is too large, so try 4. 4x4 = 16, which is
too small, so you know that the answer is somewhere between 4 and 5.

Since 25 is closer to 24 than 16, your number is probably closer
to 5. You can try 4.5 and 4.7. When you calculate 4.9x4.9 you get 24.01,
which is very close. If you want to get closer, try 4.91 or 4.89.

I hope this helps you and isn't too confusing.

Answer 4

There is a mathematical process for calculating the square root of a number, but there is no one-step formula. When set out on paper, the layout bears some resemblance to a long division sum. For long numbers, the arithmetic gets increasingly heavy as you find successive digits in the answer.

You start out by dividing the number into pairs of digits from the decimal point in both directions. You then start at the left hand end, as in long division. For each pair of digits you obtain one digit in the root. There is some estimation at each stage in the process, which involves using a 'trial divisor' with a digit missing. You have to estimate what number can be added on the end of the divisor and simultaneously placed in the root.

The method is gives successive approximations based on the identity (a+b)^2 = a^2 + 2ab + b^2.

There are other techniques, but this was the one taught in British schools in the Victorian era. Now we have calculators, it is of academic interest only.

Answer 5

In mathematics, a square root of a number x is a number whose square (the result of multiplying the number by itself) is x. Every non-negative real number x has a unique non-negative square root, called the principal square root and denoted . For example, the principal square root of 9 is 3, denoted because . The other square root of 9 (not the principal square root) is −3.

Square roots often arise when solving quadratic equations, that is equations of the form ax2 + bx + c = 0, due to the variable x being squared.

Per the fundamental theorem of algebra, there are two solutions to the equation defining the square roots of any number (although these roots may not be distinct, as in the square root of zero). For a positive real number, the two square roots are the principal square root and the negative square root (denoted ). Together, the principal and negative square roots of a number are denoted . For negative real numbers, the concept of imaginary and complex numbers has been developed to provide a mathematical framework to deal with the results. Square roots of objects other than numbers can also be defined.

Square roots of integers that are not perfect squares are always irrational numbers, i.e., numbers not expressible as a ratio of two integers. For example, cannot be written exactly as m/n, where n and m are integers. Nonetheless, it is exactly the length of the diagonal of a square with side length 1. This has been known since ancient times, with the discovery that is irrational attributed to Hippasus, a disciple of Pythagoras. (See square root of 2 for proofs.)

The square root symbol was first used during the 16th century. It has been suggested that it originated as an altered form of lowercase r, representing the Latin radix (meaning "root").

Answer 6

my algebra teacher taught me an easy way that isn't the tree thing. you see if any number times that equals a square root, for example:
the square root of 32 4 radical 2 because 16 times 2 equals 32 right? so if you split it into 2 separate radicals its radical 16 and radical 2,
since 16 can be reduced to 4 and the 2 stays as a radical then the answer is
4 rad 2 .
but idk because it involves some guessing.

Answer 7

what ever times it's self is the square root.

Answer 8

This link provides steps & examples:
http://www.bbc.co.uk/dna/h2g2/A827453

Answer 9

Yes, there is a way. It is explained here: