Importance of simplification of radical expressions before adding or subtracting

Simplifying radicals is important because basing on the root used for a number, the radical might simplify to be either a number of a radical. Only after simplification, we can know the exact irrational form of the number. When numbers are in such form, we can look for numbers with same radicals or otherwise we can look for like terms. The rules which are used with addition and subtraction of algebraic expressions can be used for radicals here treating the irrational parts as variables.

Example:

When we add  ,we cannot immediately add or subtract the terms, but extracting the numbers outside the roots and simplifying them, we have

So with simplification we can figure out like terms and combine them. So simplification is a must with radical expressions.

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