What is a perfect square? What is a square root?

A perfect square is a quadratic expression that factors into two identical binomials.

For example, if you multiply these binomials:

(x + 2)(x + 2)

You get:

x2 + 4x + 4

Therefore, the quadratic expression x2 + 4x + 4 is a perfect square since it factors into two identical binomials which are (x + 2) and (x + 2).

Notice that (x + 2)(x + 2) can be written (x + 2)2. So:

x2 + 4x + 4 = (x + 2)2

Here are some more examples of perfect squares:

x2 + 10x + 25 = (x + 5)(x + 5) = (x + 5)2

x2 - 6x + 9 = (x - 3)(x - 3) = (x - 3)2

What is a square root?

a square root of a number x is a number r such that r2 = x, or in words, a number r whose square (the result of multiplying the number by itself) is x

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