Square Roots
How do we do them?
A square root of a numberis a solution of the equation. Every number excepthas two square roots, a positive and a negative. The positive square root is theprincipal square rootand is written. To denote the negative root, writeand to indicate both roots write.
So, we callthe “square root” ofand writebecause. (See exponents for more on this.) Sincealso equalsit is also a “square root” of, but we writebecause 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 anirrational number.)
How can you estimate the value of a square root like? Well, you could first notice thatand, sinceandare both perfect squares.is in-betweenand, so. Sinceis closer tothan to,is closer to.
To find a better approximation, you can use a calculator: