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Why is it important to simplify radical expressions before adding or subtracting?

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1 Answer

Simplifying radical expressions expression is important before addition or subtraction because it you need to which like terms can be added or subtracted. 
 
An example will be the easiest way to show this:
 
3√2 + 4√18 - 6√2
 
The first and last terms are "like" terms (i.e. both are a number multiplied by the √2), so we can subtract them:
 
-3√2 + 4√18
 
At first glance, it may seem like this what the answer would be.  The remaining two terms are not "like" terms.  But, we can simplify the last term:
 
-3√2 + 4√(2*9) = -3√2 + 4√2√9 = -3√2 + (4*3)√2 = -3√2 + 12√2
 
Now, both terms are "like" terms and we can add/subtract them, giving us:
 
9√2
 
If we hadn't simplified the radical expressions, we would not have come to this solution.
 
In a way, this is similar to what would be done for polynomial expression. You are simply adding or subtracting "like" terms.

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