A rational number is a number that can be written as a ratio; which means it can be written as a fraction. 10 is a rational number because it can be written as 10/1. Any number that is not rational is considered an irrational number. An irrational number can be written as a decimal; however not a fraction. Irrational numbers also have a decimal that is not ending but it is not repeated. An example of an irrational number is pi. Pi is equal to 3.141592…….., another example is square root 2. Even though square root 2 is an irrational number, this doesn’t mean that all roots are irrational numbers.

We can also simplify roots with a higher index. An index is a number written in the “check mark” area of the radical, that indicates some other root besides a square root.

When we simplify we need to pay attention to the index. The Index is important when simplifing because that is the number of grouping that you need to take out.

We need to find groups of three when simplifying. We can simplify 162 by using a factor tree.

Then we can rewrite this under the ratical.

Pulling out the group of three and taking it to the front of the ratical leaving the 3*2 underneith the ratical.

Then we can simplify the 3*2 under the ratical.

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