Square Roots

How do we do them?

A square root of a number b is a solution of the equation x2 = b. Every number except 0 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 5 the “square root” of 25 and write because 52 = 25. (See exponents for more on this.)  Since (–5)2 also equals 25 it is also a “square root” of 25, 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 64 and 81 are both perfect squares. 70 is in-between 64 and 81, so . Since 70 is closer to 64 than to 81, is closer to 8.

To find a better approximation, you can use a calculator: