Unit 2: Day 5

Today students will learn how to add and subtract radicals.

208−−−√+52−−√

First, try to factor any perfect squares out of the radicals.

=208−−−√+52−−√

=16⋅13−−−−−√+4⋅13−−−−√

Separate the radicals and simplify.

=16−−√⋅13−−√+4√⋅13−−√

=413−−√+213−−√

Finally, simplify by combining the terms.

=(4+2)13−−√=613−−√




Since the radicals are the same, simply add the numbers in front of the radicals (do NOT add the numbers under the radicals).

Since the radicals are not the same, and both are in their simplest form, there is no way to combine these values.  The answer is the same as the problem. Warning:  If the radicals in your problem are different, be sure to check to see if the radicals can be simplified.  Often times, when the radicals are simplified, they become the same radical and can then be added or subtracted.  Always simplify, if possible, before deciding upon your answer.




Quiz

1) Simplify 2√3+3√3

2) 

Simplify:  3√4+2√4

3) 

Simplify:  2√3+3√5










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1) 

Since the radical is the same in each term (namely, the square root of three), I can combine the terms. I have two copies of the radical, added to another three copies. This gives me five copies:



2√3+3√3=(2+3) √3

             =5√3   

2) 

• Simplify:  3√4+2√4

I have three copies of the radical, plus another two copies,but I can simplify those radicals right down to whole numbers:

3√4+2√4=3x2+2x2=6+4=10

3) 

• Simplify:  2√3+3√5
These two terms have "unlike" radical parts, and I can't take anything out of either radical. Then I can't simplify the expression 2√3+3√5 any further and my answer has to be:

2√3+3√5(expression is already fully simplified)