How do we do them?
A square root of a number is a solution of the equation . Every number except has two square roots, a positive and a negative. The positive square root is the principal square root and is written . To denote the negative root, write and to indicate both roots write .
So, we call the “square root” of and write because . (See exponents for more on this.) Since also equals it is also a “square root” of , but we write because it is not the principal square root.
Not all whole numbers have a whole number square root. For instance (The decimal goes on forever and never repeats a pattern. This is called an irrational number .)
How can you estimate the value of a square root like ? Well, you could first notice that and , since and are both perfect squares. is in-between and , so . Since is closer to than to , is closer to .
To find a better approximation, you can use a calculator: