Adding and Subtracting Radicals

Date: 03/08/2001 at 22:08:38
From: Mike Edmondsom
Subject: Adding and subtracting radicals

Simplify:

  (4 Rad 6) + (2 Rad 7) + (1 Rad 24) - (1 Rad 28)

Date: 03/09/2001 at 08:27:44
From: Doctor Wolfson
Subject: Re: Adding and subtracting radicals

Hi Mike,

While you can't directly add radicals with different radicands 
(numbers under the radical), you can sometimes simplify the radicand 
so that it can be combined with another. For instance, if I asked you 
to simplify:

     (5 Rad 5) + (2 Rad 20)

20 is the same as 4 * 5, so the second term of the problem can be 
rewritten:

     (2 Rad (5 * 4))

There is a rule for radicals that

     Rad (a * b) = (Rad a) * (Rad b)

so I can again rewrite that term as:

     (2 * (Rad 5) * (Rad 4))

Rad 4 = 2, so this becomes:

     2 * Rad 5 * 2 = 4 * Rad 5.

Finally, I can combine this term with the original first term, because 
both are multiples of Rad 5:

     (5 Rad 5) + (4 Rad 5) = (9 Rad 5)

The original problem you asked is very similar, and you can use this 
method to reduce it.

I hope this helps. Feel free to write back if you'd like further 
clarification.

- Doctor Wolfson, The Math Forum
  http://mathforum.org/dr.math/