### Math

# Perfect Square Trinomial Formula | Square Root Property

Table of Contents

Perfect Square Trinomials are commonly introduced in the algebra course and it is entitled as Special Product in the Mathematics. This is named so because polynomials are grouped together in a unique way while factoring them. Here, in this post, we will discuss everything about perfect square Trinomials and how are they calculated.

### Square Footage Formula

You must be wondering what is Square Footage exactly? This is the total area occupied within a room or building. A room may be comprised of different shapes like square, rectangle, Triangle etc. Square Footage is the special unit to express the area of a room or building. Here is given Square Footage Formula for Square or Triangular area,

\[\large Square\;Footage=Length\times Breadth\]

The Square Footage Formula for a triangular area is,

\[\large Square\;Footage=\frac{Breadth\times Length}{2}\]

### Square Root Property Formula

With the basic understanding of Mathematics concepts, you must be sure what is a Square? When a number is multiplied by itself then it is named as Square. But it may sound difficult to calculate the Square Root for any particular number. It may be quite a lengthy process when numbers are given in decimals. Calculating square of nine is easy i.e. 3 but how will you calculate the square root for 5?

Here, you need to follow the lengthy process and complicated too. Don’t forget to consider the properties while calculating square roots for different numbers. With square root property formulas, it becomes easy to calculate the value with simple steps without even need for a calculator. There are multiple square root properties and we have listed only a few of them.

\[\ \sqrt{a}\cdot \sqrt{b}=\sqrt{a \times b}\]

\[\ \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\]

\[\ \sqrt{n^{2}\cdot a}=n\sqrt{a}\]

\[\ \sqrt{a}+\sqrt{b}\neq \sqrt{a+b}\]

\[\ \sqrt{a}-\sqrt{b}\neq \sqrt{a-b}\]

Based on the above properties and square root symbol, n is the index and a, b are vertices.

## Perfect Square Formula

Perfect squares in mathematics are the group of polynomials that are factored further in a convenient manner. It is also useful in solving tough mathematical equations.

\[\large \left(a+b\right)^{2}=a^{2}+2ab+b^{2}\]

#### Perfect Square Trinomials Formula

Before you understand the concept of special products – perfect square trinomials, let us first discuss some basic terminologies. A perfect square is simple that is multiplied by itself. For binomial expressions, there are only two terms are available i.e. x + 5.

When there is some algebraic expression containing more three terms then it will be named as Trinomial. For example – 5x^{2} + 5x + 4

At the same time, perfect square trinomials are special algebraic expressions that are generated when binomial is usually multiplied by itself. For example –

\[\large \left(3x+2y\right)^{2}=9x^{2}+12xy+4y^{2}\]

Once you are sure on Trinomial expressions then solving tough mathematical problems would be simpler. They are also useful in graphical problems too. As we discussed, how to convert a binomial expression in a Trinomial equation. In the same way, any trinomial equation can be reversed and converted to binomial expressions too. When you write trinomial equations then there needs to be a positive and negative version of the expression, if this is not the case then you don’t have perfect square Trinomials.The Perfect Square Trinomial Formula in mathematics is given as,

\[\large \left(ax+b\right)^{2}=(ax)^{2}+2abx+b^{2}\]

\[\large \left(ax-b\right)^{2}=(ax)^{2}-2abx+b^{2}\]