Introduction to Roots

Once you understand exponents you can begin to look at the opposite operation, finding roots. Finding the root of a number, term or expression involves going backwards by knowing the answer of an exponent expression and the power in which the original number or expression was raised to. From that information, your task is to figure out the original number. Let's start by looking at an example, taking the square root of 4.

Example:



Finding the square root of 4 is the same as saying what number to the second power = 4. We will call that number x:



If we know our exponents well we know that 2²=4. So our answer is 2:

Cubed Roots and More

We can raise a number or expression to any number of different powers, not just 2. For example we can have any of the following:

3² = 9, 4³ = 64, 10⁵ = 100,000

Just as with square roots, we can take cubed roots, 4th roots, 5th roots and even 100th roots.

Example:

Terminology

In the expression below we have three main parts:



The check mark sign is called the Radical.
The 5 is called the Index of the Radical
The 32 is called the Argument of the Radical.

Calculating Roots

While there are ways to calculate roots, most often they do not come out as a nice whole number. In the cases we have done above they did, however consider the following:



There is no way we can come up with this answer easily by just knowing what number squared is equal to 3. In fact the answer is irrational and is a never ending decimal. While there are ways to find this using pen and paper it is best to just use a calculator or a table of root values to find the answer.

If you need an exact answer it is best to leave the root in root form, in this case:



If you get the result as an answer for a practical application such as what is the length of one side of a square whose area is 3 sqft, you should round the answer:

One side of the square is approx. 1.73 ft