Simplifying Radicals

Like so much of algebra, it is good to know how to simplify radicals for purposes of canceling out or combining like terms.

Consider the square root of 27 or sqrt(27) there is no whole number that equals sqrt(27) but we can write the radical as sqrt(9*3) and that is equal to 3*sqrt(3)

Thus we have simplified the radical for purposes of mathematical calculation or canceling.

Simplifying Expressions and Combining Like Terms

In Math, like English, there is a desire to reach for simplicity and elegance when making statements.

Be as clear and short as possible to be effective.

Math expressions should be simplified, and one way to do this is to combine like terms, for example, we can realized that

2x + 3x + 2x + 10x = 27x , and it would be much better to write the shorter 27x

However

2x + 3y + 2x + 10y = 4x + 13y and that is as simple as we can get, because not all terms are like. That is to say, y is different from x and cannot be combined.

In the case of parenthesis expressions can be greatly simplified
2(2x + 4y) + 5(10x + 20y)

=

4x + 8y + 50x + 100y

=

54x + 108y

much simpler.

The ability to simplify expressions should not be underestimated. Math is used to model and describe real world problems, and its ability to be simplified allows us to draw insights from the world that would otherwise be obscured in complication.